scholarly journals Skorohod Integral at Vacuum State on Guichardet-Fock Spaces

2016 ◽  
Vol 04 (07) ◽  
pp. 1321-1326
Author(s):  
Jihong Zhang ◽  
Yongjun Li ◽  
Xiaochun Sun
Keyword(s):  
Vacuum State ◽  
Fock Spaces ◽  
Skorohod Integral

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

scholarly journals CLASSICAL MARKOV PROCESSES FROM QUANTUM LÉVY PROCESSES

1999 ◽  
Vol 02 (01) ◽  
pp. 105-129 ◽  
Author(s):  
UWE FRANZ
Keyword(s):  
Markov Process ◽  
Hopf Algebra ◽  
Markov Processes ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Markov Property ◽  
Vacuum State ◽  
Levy Processes ◽  
Quantum Process ◽  
Quantum Markov Processes

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

scholarly journals Entanglement spectrum of geometric states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Wu-zhong Guo
Keyword(s):  
Entanglement Entropy ◽  
Vacuum State ◽  
Reduced Density Matrix ◽  
Microcanonical Ensemble ◽  
Equality Case ◽  
Entanglement Spectrum ◽  
The Matrix ◽  
Point Correlation ◽  
Single Interval ◽  
Reduced Density

Abstract The reduced density matrix of a given subsystem, denoted by ρA, contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρA,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ0 which can be seen as an approximate state of ρA. The parameter λ0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞. As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.

scholarly journals EDGE CURRENTS AND VERTEX OPERATORS FOR CHERN-SIMONS GRAVITY

1993 ◽  
Vol 08 (04) ◽  
pp. 653-682 ◽  
Author(s):  
G. BIMONTE ◽  
K.S. GUPTA ◽  
A. STERN
Keyword(s):  
Boundary Conditions ◽  
Vertex Operator ◽  
Vacuum State ◽  
Space Time ◽  
Moody Algebra ◽  
Functional Integrals ◽  
Gravitational Fields ◽  
Dimensional Gravity ◽  
Discrete Mass ◽  
Chern Simons

We apply elementary canonical methods for the quantization of 2+1 dimensional gravity, where the dynamics is given by E. Witten’s ISO(2, 1) Chern-Simons action. As in a previous work, our approach does not involve choice of gauge or clever manipulations of functional integrals. Instead, we just require the Gauss law constraint for gravity to be first class and also to be everywhere differentiable. When the spatial slice is a disc, the gravitational fields can either be unconstrained or constrained at the boundary of the disc. The unconstrained fields correspond to edge currents which carry a representation of the ISO(2, 1) Kac-Moody algebra. Unitary representations for such an algebra have been found using the method of induced representations. In the case of constrained fields, we can classify all possible boundary conditions. For several different boundary conditions, the field content of the theory reduces precisely to that of 1+1 dimensional gravity theories. We extend the above formalism to include sources. The sources take into account self-interactions. This is done by punching holes in the disc, and erecting an ISO(2, 1) Kac–Moody algebra on the boundary of each hole. If the hole is originally sourceless, a source can be created via the action of a vertex operator V. We give an explicit expression for V. We shall show that when acting on the vacuum state, it creates particles with a discrete mass spectrum. The lowest mass particle induces a cylindrical space-time geometry, while higher mass particles give an n fold covering of the cylinder. The vertex operator therefore creates cylindrical space-time geometries from the vacuum.

scholarly journals Factorization and reflexivity on Fock spaces

1995 ◽  
Vol 23 (3) ◽  
pp. 268-286 ◽  
Author(s):  
Alvaro Arias ◽  
Gelu Popescu
Keyword(s):  
Fock Spaces
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