scholarly journals Canonical transformations for fermions in superanalysis

2014 ◽  
Vol 26 (06) ◽  
pp. 1450009
Author(s):  
Joachim Kupsch
Keyword(s):  
Infinite Number ◽  
Orthogonal Group ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Continuous Representation ◽  
Canonical Transformations ◽  
Module Extension ◽  
Bogoliubov Transformations

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

scholarly journals Higher spins from exotic dualisations

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nicolas Boulanger ◽  
Victor Lekeu
Keyword(s):  
Infinite Number ◽  
Arbitrary Number ◽  
Degrees Of Freedom ◽  
Young Tableaux ◽  
Spacetime Dimension ◽  
Massless Field ◽  
Free Level ◽  
Higher Spins

Abstract At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height hi by columns of height D − 2 − hi, where D is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of D − 2 extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in D = 5 and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in D = 3.

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.

Systems with Infinite Number of Degrees of Freedom

2014 ◽  
pp. 331-358
Author(s):  
Ilya Feranchuk ◽  
Alexey Ivanov ◽  
Van-Hoang Le ◽  
Alexander Ulyanenkov
Keyword(s):  
Infinite Number ◽  
Degrees Of Freedom

CLASSIFICATIONS OF KANTOWSKI–SACHS, BIANCHI TYPES I AND III SPACETIMES ACCORDING TO RICCI COLLINEATIONS

2003 ◽  
Vol 12 (01) ◽  
pp. 89-100 ◽  
Author(s):  
UĞUR CAMCI ◽  
İLHAMİ YAVUZ
Keyword(s):  
Infinite Number ◽  
Ricci Tensor ◽  
Degrees Of Freedom ◽  
Ricci Collineations ◽  
Finite Dimensional ◽  
Ricci Collineation ◽  
Special Cases ◽  
Bianchi Types

The Ricci collineation classifications of Kantowski–Sachs, Bianchi types I and III spacetimes are studied according to their degenerate and non-degenerate Ricci tensor. When the Ricci tensor is degenerate, the special cases are classified and it is shown that there are many cases of Ricci collineations (RCs) with infinite number of degrees of freedom, and the group of RCs is ten-dimensional in some spacial cases. Furthermore, it is found that when the Ricci tensor is non-degenerate, the group of RCs is finite-dimensional, and we have only either four which coincides with the isometries or six proper RCs in addition to the four isometries.

scholarly journals LOCAL EXPONENTS AND INFINITESIMAL GENERATORS OF CANONICAL TRANSFORMATIONS ON BOSON FOCK SPACES

2004 ◽  
Vol 07 (04) ◽  
pp. 547-571 ◽  
Author(s):  
F. HIROSHIMA ◽  
K. R. ITO
Keyword(s):  
Canonical Transformation ◽  
Symplectic Group ◽  
Unitary Operator ◽  
Fock Space ◽  
Adjoint Operator ◽  
The Self ◽  
Canonical Transformations ◽  
Fock Spaces ◽  
Infinitesimal Generators ◽  
Boson Fock Space

A one-parameter symplectic group {etÂ}t∈ℝ derives proper canonical transformations indexed by t on a Boson–Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of {etÂ}t∈ℝ on the Boson–Fock space and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator Δ(Â) and a local exponent [Formula: see text] with a real-valued function τÂ(·) such that [Formula: see text].

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