arXiv subjects

S. Mallik

Publications and source records attributed to S. Mallik.

71 records · Page 4Linked to original sources

arXiv2002

PT-symmetric square well and the associated SUSY hierarchies

The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength $Z$ lies below the critical value $Z_0^{\rm (crit)}$ where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of $\sec^2$-like potentials in the $Z \to 0$ limit. For $Z$ above $Z_0^{\rm (crit)}$, there is a rich diversity of SUSY hierarchies, including some with PT-symmetry breaking and some with partial PT-symmetry restoration.

quant-ph↗

arXiv2002

Spectral Representation at Finite Temperature

This is a short review on the thermal, spectral representation in the real-time version of the finite temperature quantum field theory. After presenting a clear derivation of the spectral representation, we discuss the properties of its spectral function. Two applications of this representation are then considered. One is the solution of the Dyson equation for the thermal propagator. The other is the formulation of the QCD sum rules at finite temperature.

hep-th↗

arXiv2002

Thermal QCD sum rules for mesons

A recently proposed scheme is used to saturate the spectral side of the QCD sum rules derived from the thermal, two-point correlation functions of the vector and the axial-vector currents. At low temperature, it constructs the spectral representation from all the one-loop Feynman diagrams for the two-point functions. The old saturation scheme treats incorrectly some of these contributions. We end up with the familiar QCD sum rules obtained from the difference of the two corresponding vacuum correlation functions. The possibility of obtaining new sum rules in other media is discussed.

hep-ph↗

arXiv2001

Scattering amplitude and shift in self-energy in medium

Two simple proofs are presented for the first order virial expansion of the self-energy of a particle moving through a medium, characterised by temperature and/or chemical potential(s). One is based on the virial expansion of the self-energy operator itself, while the other is on the analysis of its Feynman diagrams in configuration space.

hep-th↗

arXiv2001

Spectral representation and QCD sum rules for nucleon at finite temperature

We examine the problem of constructing spectral representations for two point correlation functions, needed to write down the QCD sum rules in the medium. We suggest constructing them from the Feynman diagrams for the correlation functions. As an example we use this procedure to write the QCD sum rules for the nucleon current at finite temperature.

hep-ph↗

arXiv2001

Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues

We analyze a set of three PT-symmetric complex potentials, namely harmonic oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a double series of energy levels along with the corresponding superpotential. Inspired by the fact that two superpotentials reside naturally in order-two parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes, we complexify their frameworks to successfully account for the three potentials.

quant-ph↗

arXiv2001

QCD sum rules for rho mesons in nuclear matter

We investigate QCD sum rules for vector currents in the rho meson channel in the nuclear medium. For increased sensitivity, we subtract out the vacuum contributions. With a saturation scheme often considered in the literature, we find these subtracted sum rules to be unstable. It indicates the importance of other contributions neglected in the saturation scheme. These include more Landau singularities at low energy, additional operators in the medium, and possibly the in-medium width of the rho meson.

hep-ph↗

arXiv2001

Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics

In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass $\wp$ type, one of them being real and the other imaginary and PT symmetric. The latter turns out to be quasiexactly solvable with one known eigenvalue corresponding to a bound state. When the Weierstrass function degenerates to a hyperbolic one, the imaginary potential becomes PT non-symmetric and its known eigenvalue corresponds to an unbound state.

quant-ph↗

arXiv1999

Rho parameters from odd and even chirality, thermal QCD sum rules

Like the even chirality correlation functions of, say, the two vector currents, one can also consider odd chirality correlation functions to write thermal QCD sum rules. They contain fewer non-perturbative corrections, at least to the leading order. Here we write such a sum rule for the correlation function of vector and tensor 'currents'. The odd and even chirality sum rules are taken together to evaluate the effective parameters of the $ρ$ meson to second order in temperature. To within errors, the results are consistent and reproduce the absence of shift in the $ρ$ meson mass to this order.

hep-ph↗

arXiv1999

Calculation of density fluctuation in inflationary epoch

Starting from an initial state of thermal equilibrium, we derive an expression for the quantum fluctuation in the energy density during the inflationary epoch in terms of the mode functions for the inflaton field. The effect of this particular initial state is not washed out in the final formula, contrary to what is usually believed. Numerically, however, the effect is completely negligible, validating the use of the two point function in the vacuum state. We also point out the requirement of conventional quantum field theory during inflation, that the quantum fluctuation in a wavelength must be evaluated, at the latest, when the wavelength crosses the Hubble length, in contrast to the usual practice in the literature.

hep-ph↗

arXiv1998

QCD sum rules at finite temperature

We derive thermal QCD sum rules for the correlation function of two vector currents in the rho-meson channel. It takes into account the leading non-perturbative corrections from the additional operators, which appear due to the breakdown of Lorentz invariance at finite temperature. The mixing of the new operators has a drastic effect on their coefficients. The thermal average of all the operators can be related to that of the quark condensate and the energy density. The sum rules then yield the temperature dependence of the parameters of the $ρ$-meson, namely its mass and coupling to the vector current. Our result is that these parameters are practically independent of temperature at least up to a temperature of 125 MeV.

hep-ph↗

arXiv1997

Operator product expansion at finite temperature

We extend an earlier, configuration space method to find the Wilson coefficients of operators appearing in the short distance expansion of thermal correlation functions of different quark bilinears. Considering all the different correlation functions, there arise, up to dimension four, two new operators, in addition to the two appearing already in the vacuum correlation functions. They would contribute substantially to the QCD sum rules, when the temperature is not too low.

hep-ph↗

arXiv1996

Density fluctuation in extended inflation

We examine the calculation of density perturbation at large scales in the inflationary scenario. The formula for its magnitude is reviewed from first principles and applied to the original model of extended inflation. Our estimate is an order of magnitude bigger than the earlier ones due to the difference in the time at which the primordial fluctuation is evaluated and to the inclusion of terms neglected earlier in the standard formula for density perturbation.

hep-ph↗

arXiv1996

Absence of second order phase transition in $ λϕ^4$ theory

We calculate the self-energy at finite temperature in scalar $λϕ^4$ theory to second order in a modified perturbation expansion. Using the renormalisation group equation to tame the logarithms in momentum, it gives an equation to determine the critical temperature. Due to the infrared freedom of the theory, this equation is satisfied, irrespective of the value of the temperature. We conclude that there is no second order phase transition in this theory.

hep-th↗

arXiv1994

Baryogenesis and damping in nonminimal electroweak models

We study the effect of damping on the generation of baryon asymmetry of the Universe in the standard model of the eletroweak theory with simple extensions of the Higgs sector. The propagation of quarks of masses up to about 5 GeV are considered, taking into account their markedly different dispersion relations due to interaction with the hot electroweak plasma. It is argued that the contribution of the b quark can be comparable to that of the t quark calculated earlier.

hep-ph↗

arXiv1994

Baryogenesis at the Electroweak Scale

The generation of the baryon asymmetry of the universe is considered in the standard model of the electroweak theory with simple extensions of the Higgs sector. The propagation of quarks of masses up to about 5 GeV are considered, taking into account their markedly different dispersion relations due to propagation through the hot electroweak plasma. It is shown that the contribution of these lighter quarks to the baryon asymmetry can be comparable to that for the t quark considered earlier.

hep-ph↗

arXiv1994

Massive States in Chiral Perturbation Theory

It is shown that the chiral nonanalytic terms generated by $Δ_{33}$ resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself.

hep-ph↗