Hilbert Space and Unitary Transformations

2019 ◽  
pp. 159-187
Author(s):  
Walter M. Wilcox
Keyword(s):  
Hilbert Space ◽  
Unitary Transformations

scholarly journals Examples of enhanced quantization: Bosons, fermions and anyons

2014 ◽  
Vol 29 (22) ◽  
pp. 1450119
Author(s):  
T. C. Adorno ◽  
J. R. Klauder
Keyword(s):  
Hilbert Space ◽  
Coherent States ◽  
Canonical Quantization ◽  
Action Functional ◽  
Classical Action ◽  
Unitary Transformations ◽  
Classical Quantum ◽  
Quantum Action ◽  
Space Vectors ◽  
Gaussian Vectors

Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which ℏ > 0 throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action functional are coherent states, which leads to the classical action functional augmented by additional terms of order ℏ. Canonical coherent states are defined by unitary transformations of a fixed, fiducial vector. While Gaussian vectors are commonly used as fiducial vectors, they cannot be used for all systems. We focus on choosing fiducial vectors for several systems including bosons, fermions and anyons.

Topological aspects of the projective unitary group

1970 ◽  
Vol 68 (1) ◽  
pp. 57-60 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Hilbert Space ◽  
Topological Group ◽  
Projective Space ◽  
Unitary Group ◽  
Principal Bundle ◽  
Strong Operator Topology ◽  
Complex Hilbert Space ◽  
Unitary Representations ◽  
Strong Operator ◽  
Unitary Transformations

1. Introduction. The group U(H) of unitary transformations of a complex Hilbert space H, endowed with its strong operator topology, is of interest in the study of unitary representations of a topological group. The unitary transformations of H induce a group U(Ĥ) of transformations of the associated projective space Ĥ. The projective unitary group U(Ĥ) with its strong operator topology is used in the study of projective (ray) representations. U(Ĥ) is, as a group, the quotient of U(H) by the subgroup S1 of scalar multiples of the identity. In this paper we prove that the strong operator toplogy of U(Ĥ) is in fact the quotient of the strong operator topology on U(H). This is related to the fact that U(H) is a principal bundle over U(Ĥ) with fibre S.

Representation of Symmetries and Observables in Functional Hilbert Space. I.

1971 ◽  
Vol 26 (4) ◽  
pp. 631-642 ◽  
Author(s):  
A. Rieckers
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Inner Product ◽  
Quantum Field ◽  
Functional Hilbert Space ◽  
Functional Formulation ◽  
Unitary Transformations ◽  
Symmetry Transformations ◽  
Symmetry Operations

Abstract A representation of symmetry transformations motivated by the functional formulation of quantum field theory is rigorously discussed in a functional Hilbert space. The set of generating functionals is equipped with an inner product by means of the Friedrichs-Shapiro-integral and completed to an Hilbert space. Unitarity, continuity, and reducibility are investigated for the symmetry operations in this space. Also non-unitary transformations are considered.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space

On Definition of Expansion Probabilistic Hilbert Space

2018 ◽  
Vol 14 (3) ◽  
pp. 59-73
Author(s):  
Ahmed Hasan Hamed ◽  
Keyword(s):  
Hilbert Space ◽  
Definition Of
Sign in / Sign up

Export Citation Format

Share Document