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We impose the periodicity conditions corresponding to the Matsubara formalism for Thermal Field Theory as constraints in the imaginary time path integral. These constraints are introduced by means of time-independent auxiliary fields which,…
This paper has been superseded by hep-th/0510131.
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent…
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…
Perturbative quantum field theory usually uses second quantisation and Feynman diagrams. The worldline formalism provides an alternative approach based on first quantised particle path integrals, similar in spirit to string perturbation…
The path-integral quantization of thermal scalar, vector and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and $\phi ^4$ theory as examples. By this quantization,…
A path integration formulation for the finite density and temperature problems is shown to be consistent with the thermodynamics using an 8 component ``real'' representation for the fermion fields by applying it to a free fermion system. A…
In this paper we develop the alternative path-integral approach to quantum mechanics. We present a resolvent of a Hamiltonian (which is Laplace transform of a evolution operator) in a form which has a sense of ``the sum over paths'' but it…
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
Proposal for contribution to the quantum field theory section in "Encyclopedia of Mathematical Physics".
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
We developed a path integral formalism for the quantum mechanics in a rotating reference of frame, and proposed a spin path integral description for the spin degrees of freedom in it. We have also give some examples for the applications of…
A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.
In a recent paper [Phys. Rev. D {\bf 72}, 085006 (2005)], Brandt {\em et al}. deduced the thermal operator representation for a thermal $N$-point amplitude, both in the imaginary-time and real-time formalisms. In the case when a chemical…
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic…
The real-time operator formalism for thermal quantum field theories, thermofield dynamics, is formulated in terms of a path-integral approach in non-commutative spaces. As an application, the two-point function for a thermal non-commutative…
We outline the nonlinear transformation in the path integral representation for partition function of O(N) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This…