etd@IISc Collection:http://hdl.handle.net/2005/372016-07-09T21:00:25Z2016-07-09T21:00:25ZTopics In Noncommutative Gauge Theories And Deformed Relativistic TheoriesChandra, Nitinhttp://hdl.handle.net/2005/24682015-08-12T10:11:55Z2015-08-11T18:30:00ZTitle: Topics In Noncommutative Gauge Theories And Deformed Relativistic Theories
Authors: Chandra, Nitin
Abstract: There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries.
In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario.
In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature.
Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics.
In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.2015-08-11T18:30:00ZModel Studies Of The Hot And Dense Strongly Interacting MatterChatterjee, Sandeephttp://hdl.handle.net/2005/25182016-04-25T12:07:36Z2016-04-24T18:30:00ZTitle: Model Studies Of The Hot And Dense Strongly Interacting Matter
Authors: Chatterjee, Sandeep
Abstract: Ultra-relativisitic heavy ion collisions produce quark gluon plasma-a hot and dense soup of deconfined quarks and gluons akin to the early universe. We study two models in the context of these collisions namely, Polyakov Quark Meson Model (PQM) and Hadron Resonance Gas Model (HRGM).The PQM Model provides us with a simple and intuitive understanding of the QCD equation of state and thermodynamics at non zero temperature and baryon density while the HRGM is the principle model to analyse the hadron yields measured in these experiments across the entire range of beam energies.
We study the effect of including the commonly neglected fermionic vacuum fluctuations to the (2+1) flavor PQM model. The conventional PQM model suffers from a rapid phase transition contrary to what is found through lattice simulations. Addition of the vacuum term tames the rapid transition and significantly improves the model’s agreement to lattice data. We further investigate the role of the vacuum term on the phase diagram. The smoothening effect of the vacuum term persists even at non zero . Depending on the value of the mass of the sigma meson, including the vacuum term results in either pushing the critical end point into higher values of the chemical potential or excluding the possibility of a critical end point altogether. We compute the fluctuations(correlations) of conserved charges up to sixth(fourth) order. Comparison is made with lattice data wherever available and overall good qualitative agreement is found, more so for the case of the normalised susceptibilities. The model predictions for the ratio of susceptibilities approach to that of an ideal gas of hadrons as in HRGM at low temperatures while at high temperature the values are close to that of an ideal gas of massless quarks.
We examine the stability of HRGMs by extending them to take care of undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that extending these models do not have much effect on hydrodynamics but the hadron yield ratios show better agreement with experiment. In principle HRGMs are internally consistent up to a temperature higher than the cross over temperature in QCD; but by examining quark number susceptibilities we find that their region of applicability seems to end even below the QCD cross over.2016-04-24T18:30:00ZProbing Higgs Boson Interactions At Future CollidersBiswal, Sudhansu Sekharhttp://hdl.handle.net/2005/9382010-11-11T20:30:24Z2010-11-10T18:30:00ZTitle: Probing Higgs Boson Interactions At Future Colliders
Authors: Biswal, Sudhansu Sekhar
Abstract: We present in this thesis a detailed analysis of Higgs boson interactions at future colliders. In particular we examine, in a model independent way, the sensitivity of an
Linear Collider in probing the interaction of Higgs boson with a pair of vector bosons with/without the use of polarized initial beams and/or the information on final state fermion polarization. We devise several observables which have definite transformation properties under discrete symmetry operations to constrain the different anomalous parts of the Higgs boson interactions having the same transformation properties. We also investigate effects of initial state radiation (ISR) and beamstrahlung on probes of anomalous Higgs boson couplings at higher center of mass energies.
We begin the first chapter with an introduction of the Standard Model (SM) of particle physics. We mainly focus on the Higgs sector of the SM. In this chapter we review the electroweak (EW) symmetry breaking mechanism, viz. the Higgs mechanism, responsible for generating masses of all the particles in the SM. We briefly summarize the high precision tests of the SM. We discuss constraints on the mass of the SM Higgs boson derived from theoretical considerations such as stability of the electroweak vacuum, unitarity in scattering amplitudes, perturbativity of the Higgs self-coupling and no fine-tuning in the radiative corrections in the Higgs sector. Next we present the experimental bounds on the mass of the SM Higgs boson obtained from the direct searches of the Higgs boson at LEP and from the electroweak high precision measurements. We then discuss the importance of a general model independent approach to study properties of the Higgs boson and to verify the uniqueness of the SM. In the context of low energy effective theory, this analysis can be made by using the effective Lagrangian that contains higher dimensional operators. We conclude this chapter giving examples of dimension-6 operators which can contribute to the anomalous Higgs boson interactions that we analyze in this thesis.
Second chapter contains the dominant Higgs boson production processes at an collider.In a model independent analysis we consider the effects of the most general
¯
(V = W Z) vertex, consistent with Lorentz invariance, for the process
where f is any light fermion. This vertex also includes the possibility of CP violation and can be written as:
where ki denote the momenta of the two W’s (Z’s), ǫναβis the antisymmetric tensor
with ǫ0123 = 1. Previous studies showed that the squared matrix element of the process e+e−ZH does not include all the anomalous parts of a general ZZH vertex. Also it is obvious that one cannot analyse anomalous WWH couplings using this process.
Hence we consider the full process e+e−ffH to probe all the anomalous parts of the
VVH vertex. We devise a general and very elegant procedure to probe these couplings at an e+e−collider. We construct various combinations by taking dot and scalar triple product of momenta of initial and final state particles. These combinations have definite transformation properties under CP and naive time reversal (T˜)transformations. Hence the corresponding observables constructed using expectation value of sign of these combinations can probe a specific part of the anomalous VVH couplings whose coefficient in the effective Lagrangian has same transformation properties. We investigate the possible sensitivity to which the anomalous VVH couplings can be probed at a Linear Collider using these observables in the process e+e−ffH for unpolarized beams [1, 2]. We consider the case of a Linear Collider, operating at center of mass energy of 500 GeV, with an integrated luminosityof 500 fb−1 and assume a Higgs boson of mass 120 GeV. We impose various kinematical cuts on different final state particles to reduce backgrounds
¯and consider the events where H decays into bb with branching ratio 0.68. We can enhance or suppress the effect of the s-channel, Z-exchange diagram by imposing cut on the ¯invariant mass of the ff system. We use b-tagging efficiency to be 70%; a value expected to be possible in the collider environment. We first consider asymmetries involving either the polar or azimuthal angular distributions. Then we combine these informations to construct combined polar-azimuthal asymmetries in order to enhance the sensitivity. We obtain strong constraints on most of the anomalous parts of the ZZH vertex using cross section and these asymmetries. The process e+eν¯
−νH has two missing ν’s in the final state. Hence their momenta are not available to construct any observables. Therefore, direct probes for T˜-odd WWH couplings viz. ℑ(bW), ℜ(˜bW), cannot be constructed and only weak, indirect bounds are possible. Further, without using polarized beams the contamination from the ZZH vertex cannot be eliminated in the determination of WWH couplings.
In the third chapter we analyze use of linearly polarized e+/e−beams and/or information on final state lepton polarization in probingthe interaction of the Higgs boson with a pair of vector bosons[3, 4]. We make several combinations of different particle momenta and spins. We then define observables as expectation values of signs of these combinations for longitudinally polarized beams and/or for production of final state τ’s with a definite helicity state. Use of polarization allows us to devise more observables as compared to the unpolarized case. We list the observables for which use of polarization affords a distinct
gain in sensitivity. In our analysis we divide the total luminosity of 500 fb−1 equally among different polarization states of initial state e−/e+ and take the values 80% and 60% for e−/e+ respectively, foreseen at the ILC. We construct numerical combinations of various linearly polarized cross sections to enhance the contribution of ℜ(bZ) while getting rid of ΔaZand vice versa. It is necessary to construct such combinations of cross section as ℜ(bZ), ΔaZhave same CP and T˜transformation properties and hence there are no asymmetries that can be constructed to probe them individually. With these combinations it is possible to probe both these CP-and T˜-even couplings cleanly, using linearly polarized beams. We find that longitudinal beam polarization can improve the sensitivity to CP-odd ZZH couplings viz. ℜ(˜bZ), ℑ(˜bZ), by a factor of about 6 −7. We also construct observables for final state τ’s with definite helicity. We make a plausible assumption that it should be possible to isolate events with τ’s in definite helicity state with an efficiency of 40%. With this assumption we demonstrate that the use of final state τ polarization can improve the sensitivity to the CP-even and T˜-odd ZZH coupling (ℑ(bZ)) by a factor of about 3. Moreover use of final state τ-polarization measurement along with linearly polarized beams can improve the sensitivity for one of the CP-odd ZZH couplings (ℜ(˜bZ))bya factor of about 2.Use of longitudinally polarized beams can also help to reduce the contamination in the measurement of the WWH couplings coming from the ZZH vertex contribution. We also perform χ2-analysis using the observables for different polarizations. The cross section of the t–channel diagram increases with increasing center of mass energy. Therefore, off hand it may look like that going to higher energy can increase the sensitivity to WWH couplings. Hence in this chapter we further investigate possible gain in sensitivity going to higher center of mass energies[3, 4]. We use the same observables constructed with unpolarized beams and consider various center of mass energies ranging from 300 GeV to 3 TeV. We find that it is possible to increase the bZ)byabouta factor 2 1 TeVas compared to the case of 500 GeV. In this analysis we include the effects of initial state radiation (ISR) and beamstrahlung. Both the ISR and beamstrahlung =500 GeV, the ISR can affect cross sections for s–channel processes by 10−15%.However, we observe that the effects of ISR and beamstrahlung change both the SM and anomalous contributions more beneficial for the study of anomalous V V H couplings.
In the last chapter we investigate the role of transversely polarized beams to constrain the anomalous V V H couplings[5]. Using transverse spin direction of e±it is possible to devise observables which are nonzero only for transversely polarized beams. Use of transverse beam polarization allows construction of completely independent probes of both the CP-and T˜-even anomalous ZZH couplings (ΔaZ, ℜ(bZ)), leading to independent determination of all the anomalous parts of the ZZH vertex. In addition the use of transverse beam polarization can also add to the sensitivity for one of the CP-odd ZZH couplings viz. ℜ(˜bZ). Measurement of final state τ-polarization with transversely polarized beams can in fact also offer improvement on the sensitivity for ℑ(bZ) which is even under CP-and odd under T˜-transformation. Use of transverse beam polarization cannot improve the bounds on the anomalous WWH couplings as the squared matrix element of the t– channel WW–fusion diagram does not have any transverse beam polarization dependent term.
A summary of the results obtained in this thesis is follows. We have developed a general procedure to construct observables with specific CP and T˜transformation properties to probe various anomalous couplings of the Higgs boson to a pair of vector bosons (V = W/Z) at an e+/e−Linear Collider. We investigate probes of these couplings in the process e+e−ffH. This process gives access to those anomalous couplings which cannot be probed using angular distribution of the Z boson in the process e+eZH.
We showed that it would be possible to obtain stringent bounds on some of the parts of the anomalous ZZH vertex even without using polarized beams and/or information on polarization of final state particles. Use of longitudinal beam polarization and/or final state τ polarization can significantly enhance the sensitivity in probing most of the anomalous parts of a general ZZH vertex. Use of longitudinal beam polarization also reduces the contamination from the ZZH couplings in the determination of the
˜T-even anomalous WWH couplings (ℜ(bW), ℑ(˜bW)). However, two missing neutrinos in the final state do not allow any direct probe of the T˜-odd WWH couplings (ℑ(bW), ℜ(˜bW)).We find that use of transverse polarization of the beams is essential to construct independent probes of the two anomalous ZZH couplings, which are even under CP and T˜transformations, viz.ΔaZand ℜ(bZ).We observed that there will be no significant gain 500 GeV), but with polarized beams is preferable from the point of view of studying anomalous V V H coupling. (For mathematical equations pl see the pdf file.)2010-11-10T18:30:00ZTransport In Quasi-One-Dimensional Quantum SystemsAgarwal, Amit Kumarhttp://hdl.handle.net/2005/11072011-04-01T20:30:30Z2011-03-31T18:30:00ZTitle: Transport In Quasi-One-Dimensional Quantum Systems
Authors: Agarwal, Amit Kumar
Abstract: This thesis reports our work on transport related problems in mesoscopic physics using analytical as well as numerical techniques. Some of the problems we studied are: effect of interactions and static impurities on the conductance of a ballistic quantum wire[1], aspects of quantum charge pumping [2, 3, 4], DC and AC conductivity of a (dissipative) quantum Hall (edge) line junctions[5, 6], and junctions of three or more Luttinger liquid (LL)quantum wires[7].
This thesis begins with an introductory chapter which gives a brief glimpse of the underlying physical systems and the ideas and techniques used in our studies. In most of the problems we will look at the physical effects caused by e-e interactions and static scattering processes.
In the second chapter we study the effects of a static impurity and interactions on the conductance of a 1D-quantum wire numerically. We use the non-equilibrium Green’s function (NEGF) formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire [1]. We study the variation of the conductance with the wire length, temperature and the strength of the impurity and electron-electron interactions. We find our numerical results to be in agreement with the results obtained from the weak interaction RG analysis. We also discover that bound states produce large density deviations at short distances and have an appreciable effect on the conductance which is not captured by the renormalization group analysis.
In the third chapter we use the equations of motion (EOM) for the density matrix and Floquet scattering theory to study different aspects of charge pumping of non-interacting electrons in a one-dimensional system. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the spectra of the charge and energy currents in the leads[2]. The EOM method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. In particular we study a system with oscillating impurities at several sites and our results agree with Floquet and adiabatic theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave in such systems. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias. We also study one-parameter charge pumping in a system where an oscillating potential is applied at one site while a static potential is applied in a different region [3]. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa.
In the fourth chapter we study the current produced in a Tomonaga-Luttinger liquid (TLL) by an applied bias and by weak, point-like impurity potentials which are oscillating in time[4]. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K−1 for spinless electrons, where Kis the interaction parameter. For K<1/2, the current grows large for special values of the bias. For non-interacting electrons with K= 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.
In chapter five, we present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Halledges corresponding to different filling factors and calculate the DC [5] and AC[6] conductivity of the system in the diffusive transport regime. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of chiral commutation relations between the outgoing bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced by Wen. The effect of density-density interactions between the two edges is considered exactly, and renormalization group (RG) ideas are used to study how the tunneling parameter changes with the length scale. The RG analysis leads to a power law variation of the conductance of the line junction with the temperature (or other energy scales) and the line junction may exhibit metallic or insulating phase depending on the strength of the interactions. Our results can be tested in bent quantum Hall systems fabricated recently.
In chapter six, we study a junction of several Luttinger Liquid (LL) wires. We use bosonization with delayed evaluation of boundary conditions for our study. We first study the fixed points of the system and discuss RG flow of various fixed points under switching of different ‘tunneling’ operators at the junction. Then We study the DC conductivity, AC conductivity and noise due to tunneling operators at the junction (perturbative).We also study the tunneling density of states of a junction of three Tomonaga-Luttinger liquid quantum wires[7]. and find an anomalous enhancement in the TDOS for certain fixed points even with repulsive e-e interactions.2011-03-31T18:30:00Z