arXiv subjects
Publications and source records attributed to F. C. Khanna.
In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed.
Finite-temperature spectra of heavy quarkonia are calculated by combining potential model and thermofield dynamics formalisms. The mass spectra of the heavy quarkonia with various quark contents are calculated. It is found that binding mass of the quarkonium decreases as temperature increases.
Analytical expressions for Bose-Einstein condensation of an ideal Bose gas analyzed within the strictures of non-extensive, generalized thermostatistics are here obtained.
In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave equations are computed such that the electric field does not induce the magnetic field and vice-versa. In a gravitational field, we analyze the Maxwell equations and the corresponding electromagnetic waves. A continuity equation is presented. A commutative and noncommutative analysis of the electromagnetic duality is described.
A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M.
The structure of an anomalous Lagrangian of the pi-rho-omega-a_1 system is investigated within the hidden local SU(2)_R x SU(2)_L symmetry approach. The interaction of the external electromagnetic and weak vector and axial-vector fields with the above hadron system is included. The Lagrangian of interest contains the anomalous Wess-Zumino term following from the well known Wess-Zumino-Witten action and six independent homogenous terms. It is characterized by four constants that are to be determined from a fit to the data on various elementary reactions. Present data allows one to extract the constants with a good accuracy. The homogenous part of the Lagrangian has been applied in the study of anomalous processes that could enhance the high energy tail of the spectrum of photons, produced in the radiative muon capture in hydrogen. It should be noted that recently, an intensive search for such enhancement processes has been carried in the literature, in an attempt to resolve the so called "g_P puzzle": an about 50 % difference between the theoretical prediction of the value of the induced pseudoscalar constant g_P and its value extracted from the high energy tail of the photon spectrum, measured in the precision TRIUMF experiment. Here, more details on the studied material are presented and new results, obtained by using the Wess-Zumino term, are provided.
The quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs is calculated within thermofield dynamics. Level statistics of the spectra is studied by plotting nearest-level spacing distribution histograms. It is found that finite temperature effects lead to a strengthening of chaotic effects, i.e. spectrum which has Poissonian distribution at zero temperature has Gaussian distribution at finite-temperature.
A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F. C. Khanna and A. E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyse the energy-momentum tensor for the Casimir effect of a free massless fermion field in a $d$-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a 3-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic boc changes sign and estimate its value when the edge of the cybe is of the order of confining lengths for baryons.
Charmed (and bottom) hypernuclei are studied in the quark-meson coupling (QMC) model. This completes systematic studies of charmed ($Λ_c^+, Σ_c, Ξ_c$), and $Λ_b$ hypernuclei in the QMC model. Effects of the Pauli blocking due to the underlying quark structure of baryons, and the $Σ_c N - Λ_c N$ channel coupling are phenomenologically taken into account at the hadronic level in the same way as those included for strange hypernuclei. Our results suggest that the $Σ_c^{++}$ and $Ξ_c^+$ hypernuclei are very unlikely to be formed, while the $Λ_c^+$, $Ξ_c^0$ and $Λ_b$ hypernuclei are quite likely to be formed. For the $Σ_c^+$ hypernuclei, the formation probability is non-zero though small. A detailed analysis is also made about the phenomenologically introduced Pauli blocking and channel coupling effects for the $Σ_c^0$ hypernuclei.
Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d \hatρ/dt \neq 0$. It is shown that the vector parameter of the invariant operator and the magnetization defined with respect to the density operator, both satisfying the quantum Liouville equation, still obey the Landau-Lifshitz-Gilbert equation.
In this work a generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermion counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F.C. Khanna and A.E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion system in a N-dimensional box in contact with a heat bath. As a particular situation we calculate the Casimir energy and pressure for the field in a 3-dimensional box. One interesting result is that the attractive or repulsive nature of the Casimir pressure can change depending on the rate among the sizes. This fact is analyzed with specific examples.
Two mode squeezed vacuum states allow Bell's inequality violation (BIQV) for all non-vanishing squeezing parameter $(ζ)$. Maximal violation occurs at $ζ\to \infty$ when the parity of either component averages to zero. For a given entangled {\it two spin} system BIQV is optimized via orientations of the operators entering the Bell operator (cf. S. L. Braunstein, A. Mann and M. Revzen: Phys. Rev. Lett. {\bf68}, 3259 (1992)). We show that for finite $ζ$ in continuous variable systems (and in general whenever the dimensionality of the subsystems is greater than 2) additional parameters are present for optimizing BIQV. Thus the expectation value of the Bell operator depends, in addition to the orientation parameters, on configuration parameters. Optimization of these configurational parameters leads to a unique maximal BIQV that depends only on $ζ.$ The configurational parameter variation is used to show that BIQV relation to entanglement is, even for pure state, not monotonic.
It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed.
We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to obtain the correlation functions both in and beyond the Hartree approximation, for the quantum mechanical analog of the $ϕ^{4}$ model. The technique involves representing the Hamiltonian in a Fock basis of annihilation and creation operators. By separating it into a solvable Gaussian part involving quadratic terms and a perturbation of quartic terms, it is possible to find the improved vacuum state to any desired order. The correlation functions for the field theory are then investigated in the Hartree approximation and those beyond the Hartree approximation are obtained by finding the improved vacuum state corrected up to ${\cal O}(λ^2)$. These correlation functions take into account next-to-leading and next-to-next-to-leading order effects in the coupling constant. We also use the Heisenberg formalism to obtain the time evolution equations for the equal-time, connected correlation functions beyond the leading order. These equations are derived by including the connected 4-point functions in the hierarchy. The resulting coupled set of equations form a part of infinite hierarchy of coupled equations relating the various connected n-point functions. The connection with other approaches based on the path integral formalism is established and the physical implications of the set of equations are discussed with particular emphasis on thermalization.
We formulate the thermofield dynamics for time-dependent systems by combining the Liouville-von Neumann equation, its invariant operators, and the basic notions of thermofield dynamics. The new formulation is applied to time-dependent bosons and fermions by using the time-dependent annihilation and creation operators that satisfy the Liouville-von Neumann equation. It is shown that the thermal state is the time- and temperature-dependent vacuum state and a general formula is derived to calculate the thermal expectation value of operators.
The binding energy spectra of the heavy quarkonia are calculated by solving the Schrödinger equations with Coulomb plus confining potentials. Statistical properties of the obtained spectra are studied by plotting nearest level spacing distribution histograms.
Classical regular and chaotic dynamics of the particle bound in the Coulomb plus linear potential under the influence of time-periodical perturbations is treated using resonace analysis. Critical value of the external field at which chaotization will occur is evaluated analytically based on the Chirikov criterion of stochasticity.
The temperature and density dependence of the meson-nucleon vertex form factors is studied in the framework of thermofield dynamics. Results are obtained for two rather different nucleon-nucleon potentials: the usual Bonn potential and the variation with a softer $πNN$ form factor, due to Holinde and Thomas. In general, the results show only a modest degree of sensitivity to the choice of interaction.