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F. C. Khanna

Publications and source records attributed to F. C. Khanna.

At least 19 recordsLinked to original sources
arXiv2024

Symplectic Representation of the Ginzburg-Landau Theory

In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function, i.e., a Wigner-type function. The starting point is the thermal group representation of Euclidean symmetries and gauge symmetry. Well-known basic results on the behavior of a superconductor are re-derived, providing the consistency of representation. The critical superconducting current density is determined and its usual behavior is inferred. The negativety factor associated with the quasi-distribution function is analyzed, providing information about the non-classicality nature of the superconductor state in the region closest to the edge of the superconducting material.

cond-mat.supr-con↗
arXiv2020

Spin-1/2 particles in Phase space: Casimir effect and Stefan-Boltzmann law at finite temperature

The Dirac field, spin 1/2 particles, is investigated in phase space. The Dirac propagator is defined. The Thermo Field Dynamics (TFD) formalism is used to introduce finite temperature. The energy-momentum tensor is calculated at finite temperature. The Stefan-Boltzmann law is established and the Casimir effect is calculated for the Dirac field in phase space at zero and finite temperature. A comparative analysis with these results in standard quantum mechanics space is realized.

hep-th↗
arXiv2019

Zeeman Effect in Phase Space

The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using solution of the Schrödinger equation in phase space the Wigner function related to the Zeeman effect is calculated. For this purpose, the Bohlin mapping is used to transform the Coulomb potential into a harmonic oscillator problem. Then it is possible to solve the Schrödinger equation easier by using the perturbation theory. The negativity parameter for this system is realised.

quant-ph↗
arXiv2019

Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

hep-th↗
arXiv2019

On Gravitational Casimir Effect and Stefan-Boltzmann Law at Finite Temperature

Gravitons are described by the propagator in Teleparallel gravity in nearly flat space-time. Finite temperature is introduced by using Thermo Field Dynamics formalism. The Gravitational Casimir effect and Stefan-Boltzmann law are calculated as a function of temperature. Then an equation of state for gravitons is determined.

hep-th↗
arXiv2019

On Lorentz violation in $e^{-}\!\!+\!e^{+}\!\rightarrow\!μ^{-}\!\!+\!μ^{+}$ scattering at finite temperature

Small violation of Lorentz and CPT symmetries may emerge in models unifying gravity with other forces of nature. An extension of the standard model with all possible terms that violate Lorentz and CPT symmetries are included. Here a CPT-even non-minimal coupling term is added to the covariant derivative. This leads to a new interaction term that breaks the Lorentz symmetry. Our main objective is to calculate the cross section for the $e^{-}\!\!+\!e^{+}\!\rightarrow\!μ^{-}\!\!+\!μ^{+}$ scattering in order to investigate any violation of Lorentz and/or CPT symmetry at finite temperature. Thermo Field Dynamics formalism is used to consider finite temperature effects.

hep-th↗
arXiv2016

On a group-theoretical approach to the curl operator

We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the curl operator is constructed and its action is extended to a complex plane. This scheme allows us to obtain properties, similar to those of the traditional curl operator.

math-ph↗
arXiv2016

Hénon-Heiles Interaction for Hydrogen Atom in Phase Space

Using elements of symmetry, as gauge invariance, several aspects of a Schrödinger equation represented in phase-space are introduced and analyzed under physical basis. The Hydrogen atom is explored in the same context. Then we add a Hénon-Heiles potential to the Hydrogen atom in order to explore chaotic features.

quant-ph↗
arXiv2015

Path-integral quantization of Galilean Fermi fields

The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to the Galilean Dirac equation, which leads to the Levy-Leblond equations, and define the Galilean generating functional and Green's functions for positive- and negative-energy/mass solutions. Then, as an example of interactions, we consider the quartic self-interacting potential $λ (\barΨ Ψ)^2$, and we derive expressions for the 2- and 4-point Green's functions. Our results are compatible with those found in the literature on non-relativistic many-body systems. The extended manifold allows for compact expressions of the contributions in $(3+1)$ space-time. This is particularly apparent when we represent the results with diagrams in the extended $(4+1)$ manifold, since they usually encompass more diagrams in Galilean $(3+1)$ space-time.

hep-th↗
arXiv2014

Schwarzschild-type solution in an effective gravitational theory with local Galilean invariance

We construct a Schwarzschild-type exact external solution for a theory of gravity admitting local Galilean invariance. In order to realize the Galilean invariance we need to adopt a five-dimensional manifold. The solution for the gravitational field equations obeys a Birkhoff-like theorem. Three classic tests of general relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The Galilean version of these tests exhibits an additional parameter $b$ related to the fifth-coordinate. This constant $b$ can be estimated by a comparison with observational data. We observe that the Galilean theory is able to reproduce the results traditionally predicted by general relativity in the limit of negligible $b$. This shows that the tests are not specifically Lorentz invariant.

gr-qc↗
arXiv2014

Quantum field theory on toroidal topology: algebraic structure and applications

The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particles physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matted physics.

hep-th↗
arXiv2014

Classic tests of General Relativity described by brane-based spherically symmetric solutions

We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in details: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter $b$ related to the fifth-coordinate. This constant $b$ can be constrained by comparison with observational data for massive and massless particles.

gr-qc↗
arXiv2014

Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space

Representations of the Poincaré symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability density). The gauge symmetry analysis provides a realization of the Seiberg-Witten gauge theory for noncommutative fields.

hep-th↗
arXiv2012

Phase transition in the massive Gross-Neveu model in toroidal topologies

We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-$N$ coupling constant ($g$), investigating its dependence on the compactification length ($L$) and the temperature ($T$). For all values of the fixed coupling constant ($λ$), we find an asymptotic-freedom type of behavior, with $g\to 0$ as $L\to 0$ and/or $T\to \infty$. At T=0, and for $λ\geq λ_{c}^{(D)}$ (the strong coupling regime), we show that, starting in the region of asymptotic freedom and increasing $L$, a divergence of $g$ appears at a finite value of $L$, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, $L_{c}^{(D)}$, and the deconfining temperature, $T_{d}^{(D)}$, are determined as functions of $λ$ and the mass ($m$) of the fermions, in the case of $D=2,3,4$. Taking $m$ as the constituent quark mass ($\approx 350\: MeV$), the results obtained are of the same order of magnitude as the diameter ($\approx 1.7 fm$) and the estimated deconfining temperature ($\approx 200\: MeV$) of hadrons.

hep-th↗
arXiv2011

Classical and Quantum Mechanical State Reconstruction

We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging known as Computer Aided Tomography. We explain how this method can be taken over to quantum mechanics, where it leads to a description of the quantum state in terms of the Wigner function which, although may take on negative values, plays the role of the probability density in phase space in classical physics. We explain another approach to quantum state reconstruction based on the notion of Mutually Unbiased Bases, and indicate the relation between these two approaches. Both are for a continuous, infinite-dimensional Hilbert space. We then study the finite-dimensional case and show how the second method, based on Mutually Unbiased Bases, can be used for state reconstruction.

quant-ph↗
arXiv2011

Quantum fields in toroidal topology

The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ Γ_{D}^{d}=(\mathbb{S}^{1})^{d}\times \mathbb{M}^{D-d}$. The modular operator is generalized to introduce representations of isometry groups. The Poincaré symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space-time, that follows as a generalization of the Fourier-integral representation of the propagator at finite temperature. An important result is that the $2\times2$ representation of the real time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We analyze initially the free Klein-Gordon and Dirac fields, and then formulate non-abelian gauge theories in $Γ_{D}^{d}$. Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification.

hep-th↗
arXiv2011

Teleparallel formalism of galilean gravity

A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant equations. In addition, this Galilei teleparallel approach provides a prescription to couple the 5-bein field to the galilean covariant Dirac field.

gr-qc↗