Related papers: General Unitary SU(1,1) TFD Formulation
A generalization of the Thermo Field Dynamics (TFD) for fermionic degrees of freedom is proposed. Such a generalization follows a previous one where the SU(1,1) thermal group was used to obtain the closed bosonic string at finite…
All possible Bogoliubov operators that generate the thermal transformations in the Thermo Field Dynamics (TFD) form a SU(1,1) group. We discuss this contruction in the bosonic string theory. In particular, the transformation of the Fock…
The thermal Bogoliubov transformation in thermo field dynamics is generalized in two respects. First, a generalization of the $\alpha$--degree of freedom to tilde non--conserving representations is considered. Secondly, the usual $2\times2$…
Thermal Bogoliubov transformation is an essential ingredient of the thermo field dynamics -- the real time formalism in quantum field and many-body theories at finite temperatures developed by H. Umezawa and coworkers. The approach to study…
In this Letter a topological interpretation for the string thermal vacuum in the Thermo Field Dynamics (TFD) approach is given. As a consequence, the relationship between the Imaginary Time and TFD formalisms is achieved when both are used…
The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction and long-range particle-hole effective forces…
A generalization of Ojima tilde conjugation rules is suggested, which reveals the coherent state properties of thermal vacuum state and is useful for the thermofield bosonization. The notion of hot and cold thermofields is introduced to…
The Thermo Field Dynamics formalism is presented. In particular, it is applied to the two-dimensional field theory that describes a open bosonic string. The value of entropy operator is computed in various Dirichlet and Neumann boundary…
We study the Tavis-Cummings model with three modes of oscillation by using four different algebraic methods: the Bogoliubov transformation, the normal-mode operators, and the tilting transformation of the $SU(1,1)$ and $SU(2)$ groups. The…
The standard Bogoliubov transformation is generalized to enable fermion number parity breaking. The new transformation can diagonalize fermion Hamiltonians that are quadratic in fermion and number parity operators. This new variational…
In the preceding paper arXiv:0802.3252 [quant-ph] we treated a model given by a master equation with generalized Lindblad form, and examined the algebraic structure related to some Lie algebras and constructed an approximate solution. In…
Although the thermofield dynamics (TFD) was developed specifically for systems to which the ladder canonical operators and are associated, in the paper we showed that this approach can also be formulated for systems of deformed bosons,…
We construct a Gr\"obner-Shirshov basis of the Temperley-Lieb algebra $\mathfrak{T}(d,n)$ of the complex reflection group $G(d,1,n)$, inducing the standard monomials expressed by the generators $\{E_i\}$ of $\mathfrak{T}(d,n)$. This result…
The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum-field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar…
We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in $1+1$ spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely…
The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light…
Thermofield dynamics (TFD) is a powerful framework to account for thermal effects in a wavefunction setting, and has been extensively used in physics and quantum optics. TFD relies on a duplicated state space and creates a correlated…
Unitarily implementable Bogoliubov transformations for charged, relativistic bos\-ons and fermions are discussed, and explicit formulas for the 2-cocycles appearing in the group product of their implementers are derived. In the fermion case…
We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms…
The generalized massive Thirring model (GMT) with $N_{f}(=$number of positive roots of $su(n)$) fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized…