scholarly journals Inequivalent representations in the functional integral framework

2017 ◽  
Vol 804 ◽  
pp. 012006 ◽  
Author(s):  
M Blasone ◽  
P Jizba ◽  
L Smaldone
Keyword(s):  
Functional Integral ◽  
Inequivalent Representations

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

Fuzzy Bezier splines with application to fuzzy functional integral equations

2020 ◽  
Vol 24 (8) ◽  
pp. 6069-6084
Author(s):  
Alexandru Mihai Bica ◽  
Constantin Popescu
Keyword(s):  
Integral Equations ◽  
Functional Integral ◽  
Functional Integral Equations

THE FUNCTIONAL INTEGRAL ON THE HALF-LINE

1990 ◽  
Vol 05 (15) ◽  
pp. 3029-3051 ◽  
Author(s):  
EDWARD FARHI ◽  
SAM GUTMANN
Keyword(s):  
Time Evolution ◽  
Wide Class ◽  
Green's Functions ◽  
Green’S Functions ◽  
Functional Integral ◽  
Half Line ◽  
Functional Integrals ◽  
Quantum Hamiltonian ◽  
Do So

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

An unified approach to inelastic light scattering in Keldysh–Schwinger functional integral formalism

2015 ◽  
Vol 29 (07) ◽  
pp. 1550040 ◽  
Author(s):  
Hyun Cheol Lee
Keyword(s):  
Light Scattering ◽  
Cross Sections ◽  
Golden Rule ◽  
Functional Integral ◽  
Integral Formalism ◽  
Inelastic Light Scattering ◽  
Scattering Geometry ◽  
The One ◽  
Resonant Part ◽  
Functional Integral Formalism

We propose a theoretical framework which can treat the nonresonant and the resonant inelastic light scattering on an equal footing in the form of correlation function, employing Keldysh–Schwinger functional integral formalism. The interference between the nonresonant and the resonant process can be also incorporated in this framework. This approach is applied to the magnetic Raman scattering of two-dimensional antiferromagnetic insulators. The entire set of the scattering cross-sections are obtained at finite temperature, the result for the resonant part agrees with the one obtained by the conventional Fermi golden rule at zero temperature. The interference contribution is shown to be very sensitive to the scattering geometry and the band structure.

scholarly journals Functional integral formulations for classical fluids

2001 ◽  
Vol 114 (13) ◽  
pp. 5637-5641 ◽  
Author(s):  
Hyung-June Woo ◽  
Xueyu Song
Keyword(s):  
Functional Integral ◽  
Classical Fluids

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

Reaction diffusion with initially separated reactants: Functional integral approach

1997 ◽  
Vol 56 (1) ◽  
pp. 708-711 ◽  
Author(s):  
Victor Malyutin ◽  
Savely Rabinovich ◽  
Shlomo Havlin
Keyword(s):  
Reaction Diffusion ◽  
Functional Integral ◽  
Integral Approach

scholarly journals On gauge independence for gauge models with soft breaking of BRST symmetry

2014 ◽  
Vol 29 (30) ◽  
pp. 1450184 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Landau Gauge ◽  
Functional Integral ◽  
Yang Mills ◽  
Gauge Models ◽  
S Matrix ◽  
Gauge Fixing ◽  
Dependent Parameter ◽  
Quantum Treatment

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

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