scholarly journals ON POSSIBLE GENERALIZATIONS OF FIELD-ANTIFIELD FORMALISM

1993 ◽  
Vol 08 (13) ◽  
pp. 2333-2350 ◽  
Author(s):  
I. A. BATALIN ◽  
I. V. TYUTIN
Keyword(s):  
Phase Space ◽  
Master Equation ◽  
Jacobian Matrix ◽  
Functional Integral ◽  
Quantum Master Equation ◽  
Arbitrary Field ◽  
Constraint Surface

A generalized version is proposed for the field–antifield formalism. The antibracket operation is defined in arbitrary field–antifield coordinates. The antisymmetric definitions are given for first- and second-class constraints. In the case of second-class constraints the Dirac's antibracket operation is defined. The quantum master equation as well as the hypergauge fixing procedure are formulated in a coordinate–invariant way. The general hypergauge functions are shown to be antisymmetric first–class constraints whose Jacobian matrix determinant is constant on the constraint surface. The BRST-type generalized transformations are defined and the functional integral is shown to be independent of the hypergauge variations admitted. In the case of reduced phase space the Dirac's antibrackets are used instead of the ordinary ones.

scholarly journals QUANTIZATION OF THE TOPOLOGICAL σ-MODEL AND THE MASTER EQUATION OF THE BV FORMALISM

1994 ◽  
Vol 09 (06) ◽  
pp. 491-500 ◽  
Author(s):  
S. AOYAMA
Keyword(s):  
Phase Space ◽  
Master Equation ◽  
Symplectic Structure ◽  
Kähler Manifold ◽  
Quantum Master Equation ◽  
Kahler Manifold ◽  
Invariant States

We quantize the topological σ-model. The quantum master equation of the Batalin-Vilkovisky formalism ΔρΨ=0 appears as a condition which eliminates the exact states from the BRST invariant states Ψ defined by QΨ=0. The phase space of the BV formalism is a supermanifold with a specific symplectic structure, called the fermionic Kähler manifold.

scholarly journals COVARIANT DESCRIPTION OF PARAMETRIZED NONRELATIVISTIC HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (15) ◽  
pp. 2473-2493 ◽  
Author(s):  
MAURICIO MONDRAGÓN ◽  
MERCED MONTESINOS
Keyword(s):  
Phase Space ◽  
Gauge Transformation ◽  
Hamiltonian Systems ◽  
Symplectic Structure ◽  
Canonical Formalism ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Algebra Of Observables ◽  
Covariant Description ◽  
Constraint Surface

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

scholarly journals Quantum measurement of a solid-state qubit: A unified quantum master equation approach

2004 ◽  
Vol 69 (8) ◽  
Author(s):  
Xin-Qi Li ◽  
Wen-Kai Zhang ◽  
Ping Cui ◽  
Jiushu Shao ◽  
Zhongshui Ma ◽  
...  
Keyword(s):  
Solid State ◽  
Master Equation ◽  
Quantum Measurement ◽  
Quantum Master Equation ◽  
Equation Approach ◽  
Master Equation Approach

Quantum statistical physics: Functional integration formalism

2021 ◽  
pp. 64-89
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Phase Space ◽  
Integral Representation ◽  
Density Matrix ◽  
Thermal Equilibrium ◽  
Degrees Of Freedom ◽  
Functional Integral ◽  
Complex Variables ◽  
Path Integral Representation ◽  
Canonical Formulation ◽  
Grand Canonical

The functional integral representation of the density matrix at thermal equilibrium in non-relativistic quantum mechanics (QM) with many degrees of freedom, in the grand canonical formulation is introduced. In QM, Hamiltonians H(p,q) can be also expressed in terms of creation and annihilation operators, a method adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism, quantum operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables that correspond in the classical limit to a complex parametrization of phase space. The formalism is adapted to the description of many-body boson systems. To this formalism corresponds a path integral representation of the density matrix at thermal equilibrium, where paths belong to complex spaces, instead of the more usual position–momentum phase space. A parallel formalism can be set up to describe systems with many fermion degrees of freedom, with Grassmann variables replacing complex variables. Both formalisms can be generalized to quantum gases of Bose and Fermi particles in the grand canonical formulation. Field integral representations of the corresponding quantum partition functions are derived.

Neural network representation and optimization of thermoelectric states of multiple interacting quantum dots

2020 ◽  
Vol 22 (28) ◽  
pp. 16165-16173
Author(s):  
Hangbo Zhou ◽  
Gang Zhang ◽  
Yong-Wei Zhang
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Quantum Dots ◽  
Seebeck Coefficient ◽  
Master Equation ◽  
Thermoelectric Properties ◽  
Electrical Conductance ◽  
Thermal Conductance ◽  
Quantum Master Equation ◽  
Network Representation

We perform quantum master equation calculations and machine learning to investigate the thermoelectric properties of multiple interacting quantum dots, including electrical conductance, Seebeck coefficient, thermal conductance and ZT.

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