scholarly journals Spinfoams in the holomorphic representation

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
Eugenio Bianchi ◽  
Elena Magliaro ◽  
Claudio Perini
Keyword(s):  
Holomorphic Representation

scholarly journals Coherent representation of fields and deformation quantization

2020 ◽  
Vol 17 (11) ◽  
pp. 2050166 ◽  
Author(s):  
Jasel Berra-Montiel ◽  
Alberto Molgado
Keyword(s):  
Phase Space ◽  
Deformation Quantization ◽  
Probability Distributions ◽  
Series Representation ◽  
Quantum Field ◽  
Husimi Distribution ◽  
Normal Star ◽  
Holomorphic Representation ◽  
Functional Distribution ◽  
Space Description

Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows to establish a [Formula: see text]-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution, which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

COHERENT STATES WITHOUT GROUPS: QUANTIZATION ON NONHOMOGENEOUS MANIFOLDS

1993 ◽  
Vol 08 (18) ◽  
pp. 1735-1738 ◽  
Author(s):  
JOHN R. KLAUDER
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
Wide Class ◽  
Coherent States ◽  
Path Integrals ◽  
Killing Vector ◽  
Single Variable ◽  
Holomorphic Representation ◽  
Representation Spaces ◽  
State Path

A wide class of single-variable holomorphic representation spaces are constructed that are associated with very general sets of coherent states defined without the use of transitively acting groups. These representations and states are used to define coherent-state path integrals involving phase-space manifolds having one Killing vector but a quite general curvature otherwise.

Quantum Teleportation and Holomorphic Representation of CCR

2008 ◽  
Vol 15 (02) ◽  
pp. 155-172 ◽  
Author(s):  
S. Nagamachi ◽  
E. Brüning
Keyword(s):  
Quantum Teleportation ◽  
Wigner Functions ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Holomorphic Representation

For the treatment of teleportation of continuous quantum variables, often the Wigner functions are used. In this paper, we will show that by using the holomorphic representation of the canonical commutation relations (CCR), the teleportation of continuous quantum variables is treated in a parallel way as the teleportation of qubits.

GAUGE-INVARIANT QUANTISATION OF CHIRAL GAUGE THEORIES

1990 ◽  
Vol 05 (03) ◽  
pp. 175-182 ◽  
Author(s):  
T. D. KIEU
Keyword(s):  
Path Integral ◽  
Gauge Theories ◽  
Berry Phase ◽  
Integral Functional ◽  
Gauge Fields ◽  
Quantum Mechanical ◽  
Gauge Invariant ◽  
Normal Ordering ◽  
Schwinger Model ◽  
Holomorphic Representation

The path-integral functional of chiral gauge theories with background gauge potentials are derived in the holomorphic representation. Justification is provided, from first quantum mechanical principles, for the appearance of a functional phase factor of the gauge fields in order to maintain the gauge invariance. This term is shown to originate either from the Berry phase of the first-quantized hamiltonians or from the normal ordering of the second-quantized hamiltonian with respect to the Dirac in-vacuum. The quantization of the chiral Schwinger model is taken as an example.

scholarly journals A HOLOMORPHIC REPRESENTATION OF THE JACOBI ALGEBRA

2006 ◽  
Vol 18 (02) ◽  
pp. 163-199 ◽  
Author(s):  
STEFAN BERCEANU
Keyword(s):  
Hilbert Space ◽  
Differential Operators ◽  
Holomorphic Functions ◽  
First Order ◽  
Polynomial Coefficients ◽  
Holomorphic Representation

A representation of the Jacobi algebra 𝔥1 ⋊ 𝔰𝔲(1, 1) by first-order differential operators with polynomial coefficients on the manifold [Formula: see text] is presented. The Hilbert space of holomorphic functions on which the holomorphic first-order differential operators with polynomials coefficients act is constructed.

Holomorphic representation theory. I

1995 ◽  
Vol 301 (1) ◽  
pp. 155-181 ◽  
Author(s):  
Karl-Hermann Neeb
Keyword(s):  
Representation Theory ◽  
Holomorphic Representation
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