arXiv subjects

Dipankar Chakrabarti

Publications and source records attributed to Dipankar Chakrabarti.

63 records · Page 4Linked to original sources

arXiv2005

A transition in the spectrum of the topological sector of $ϕ_2^4$ theory at strong coupling

We investigate the strong coupling region of the topological sector of the two-dimensional $ϕ^4$ theory. Using discrete light cone quantization (DLCQ), we extract the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluate the expectation value of the integral of the normal ordered $ϕ^2$ operator and we extract the number density of constituents in these states. A coherent state variational calculation confirms that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation is extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrate that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extract the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpret the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional $ϕ^4$ theory.

hep-th↗

arXiv2004

Non-perturbative Studies in Quantum Chromodynamics

In this thesis, two nonperturbative techniques, namely, similarity renormalization group (SRG) approach and light-front transverse lattice (LFTL) approach are studied in the the context of hadron bound state problem in light-front QCD. We first investigate the meson bound state problem in (2+1) dimensional QCD using Bloch effective Hamiltonian which serves as a benchmark for comparative study of the SRG Hamiltonian. In the SRG scheme we compare three different choices for the similarity factor. In (2+1) dimensions, in the lowest order, SRG produces linear confinement along the transverse direction but only square root confinement along the longitudinal direction and thus breaks the rotational symmetry. In the LFTL approach, we first investigate the problem associated with fermion formulation on a LFTL. When the symmetric lattice derivative is used, the doublers arise due to decoupling of even and odd sub-lattices. We have discussed Wilson fermion and staggered fermion to remove the doublers. We propose another way of formulating fermions on LFTL by using asymmetric lattice derivatives in such a way that the Hermiticity of the Hamiltonian is preserved. There are no doublers in this method. We also discuss the symmetry relevant for fermion doubling on LFTL. We also compare these two methods of fermion formulations in the context of meson bound state problem in (3+1) dimensional QCD with at most one link approximation.

hep-th↗

arXiv2003

Kinks in Discrete Light Cone Quantization

We investigate non-trivial topological structures in Discrete Light Cone Quantization (DLCQ) through the example of the broken symmetry phase of the two dimensional $ϕ^4$ theory using anti periodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi - classical results. We compare the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state.

hep-th↗

arXiv2003

A study of $q {\bar q}$ states in transverse lattice QCD using alternative fermion formulations

In this work we investigate $q{\bar q}$ spectra and wavefunctions of light front transverse lattice Hamiltonians that result from different methods of formulating fermions on the transverse lattice. We adopt the one link approximation for the transverse lattice and Discrete Light Cone Quantization to handle longitudinal dynamics. We perform a detailed study of the continuum limit of DLCQ and associated techniques to manage severe light front infrared divergences. We explore the effects of various parameters of the theory, especially, the strength of the helicity-flip interaction and the link mass on spectra and wavefunctions.

hep-ph↗

arXiv2002

Fermions on the light front transverse lattice

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and backward derivatives. There is no fermion doubling and the helicity flip term proportional to the fermion mass in the full light front QCD becomes an irrelevant term in the free field limit. In the second approach with symmetric derivative (which has been employed previously in the literature), doublers appear and their occurrence is due to the decoupling of even and odd lattice sites. We study their removal from the spectrum in two ways namely, light front staggered formulation and the Wilson fermion formulation. The numerical calculations in free field limit are carried out with both fixed and periodic boundary conditions on the transverse lattice and finite volume effects are studied. We find that an even-odd helicity flip symmetry on the light front transverse lattice is relevant for fermion doubling.

hep-th↗

arXiv2001

Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach

Recently we have studied the Bloch effective Hamiltonian approach to bound states in 2+1 dimensional gauge theories. Numerical calculations were carried out to investigate the vanishing energy denominator problem. In this work we study similarity renormalization approach to the same problem. By performing analytical calculations with a step function form for the similarity factor, we show that in addition to curing the vanishing energy denominator problem, similarity approach generates linear confining interaction for large transverse separations. However, for large longitudinal separations, the generated interaction grows only as the square root of the longitudinal separation and hence produces violations of rotational symmetry in the spectrum. We carry out numerical studies in the Głazek-Wilson and Wegner formalisms and present low lying eigenvalues and wavefunctions. We investigate the sensitivity of the spectra to various parameterizations of the similarity factor and other parameters of the effective Hamiltonian, especially the scale $σ$. Our results illustrate the need for higher order calculations of the effective Hamiltonian in the similarity renormalization scheme.

hep-th↗

arXiv2001

Mesons in Light-Front QCD$_{2+1}$: Investigation of a Bloch Effective Hamiltonian

We study the meson sector of 2+1 dimensional light-front QCD using a Bloch effective Hamiltonian in the first non-trivial order. The resulting two dimensional integral equation is converted into a matrix equation and solved numerically. We investigate the efficiency of Gaussian quadrature in achieving the cancellation of linear and logarithmic light-front infrared divergences. The vanishing energy denominator problem which leads to severe infrared divergences in 2+1 dimensions is investigated in detail. Our study indicates that in the context of Fock space based effective Hamiltonian methods to tackle gauge theories in 2+1 dimensions, approaches like similarity renormalization method may be mandatory due to uncanceled infrared divergences caused by the vanishing energy denominator problem. We define and study numerically a reduced model which is relativistic, free from infrared divergences, and exhibits logarithmic confinement. The manifestation and violation of rotational symmetry as a function of the coupling are studied quantitatively.

hep-th↗

arXiv2001

Quark Transversity Distribution in Perturbative QCD: Light-Front Hamiltonian Approach

To resolve the current ambiguity in the splitting function corresponding to the quark transversity distribution $h_1(x)$, we calculate $h_1(x)$ for a dressed quark in light-front Hamiltonian perturbation theory. Our result agrees with the expected form of the splitting function found in the literature and disagrees with the recent calculation in \cite{kuhn}. We emphasize the importance of quark mass in $h_1(x)$ in perturbative QCD and show its connection with a part of $g_T$.

hep-ph↗

arXiv2000

A Numerical Experiment in DLCQ: Microcausality, Continuum Limit and all that

Issues related with microcausality violation and continuum limit in the context of (1+1) dimensional scalar field theory in discretized light-cone quantization (DLCQ) are addressed in parallel with discretized equal time quantization (DETQ) and the fact that Lorentz invariance and microcausality are restored if one can take the continuum limit properly is emphasized. In the free case, it is shown with numerical evidence that the continuum results can be reproduced from DLCQ results for the Pauli-Jordan function and the real part of Feynman propagator. The contributions coming from $k^+$ near zero region in these cases are found to be very small in contrast to the common belief that $k^+=0$ is an accumulation point. In the interacting case, aspects related to the continuum limit of DLCQ results in perturbation theory are discussed.

hep-th↗