scholarly journals W-ALGEBRAS FROM HEISENBERG CATEGORIES

2016 ◽  
Vol 17 (5) ◽  
pp. 981-1017 ◽  
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Anthony M. Licata ◽  
Joshua Sussan
Keyword(s):  
Symmetric Functions ◽  
Fock Space ◽  
Hochschild Homology ◽  
Space Representation

The trace (or zeroth Hochschild homology) of Khovanov’s Heisenberg category is identified with a quotient of the algebra$W_{1+\infty }$. This induces an action of$W_{1+\infty }$on the center of the categorified Fock space representation, which can be identified with the action of$W_{1+\infty }$on symmetric functions.

Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

2006 ◽  
Vol 13 (04) ◽  
pp. 415-426 ◽  
Author(s):  
P. Aniello ◽  
C. Lupo ◽  
M. Napolitano
Keyword(s):  
Lie Algebras ◽  
Fock Space ◽  
Fixed Number ◽  
Unitary Groups ◽  
Space Representation ◽  
Remarkable Case ◽  
Mathematical Structures ◽  
Passive Devices ◽  
Optical Modes ◽  
Linear Optical

In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U (N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.

scholarly journals A TWO-PARAMETER DEFORMED SUSY ALGEBRA FOR SUp/q(n)-COVARIANT (p,q)-DEFORMED FERMIONIC OSCILLATORS

2005 ◽  
Vol 20 (08) ◽  
pp. 613-622 ◽  
Author(s):  
ABDULLAH ALGIN ◽  
METIN ARIK
Keyword(s):  
Quantum Group ◽  
Fock Space ◽  
Space Representation ◽  
Oscillator Algebra ◽  
Two Parameter

We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SU p/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

ON THE FOCK SPACE REPRESENTATION OF THE WITTEN VERTEX

1994 ◽  
Vol 09 (06) ◽  
pp. 465-477
Author(s):  
RAINER DICK
Keyword(s):  
Closed Form ◽  
Fock Space ◽  
Closed String ◽  
Space Representation ◽  
Operator Representations

The bosonic overlap conditions for operator representations of the Witten vertex and its closed string analog are solved in closed form for arbitrary many external strings. This is accomplished by the use of transformed operator bases of the strings. In particular, the bosonic factor of the Witten vertex for three closed strings is realized in Fock space.

Symplectic Schrödinger equation for many-body systems

2020 ◽  
Vol 35 (06) ◽  
pp. 2050033
Author(s):  
R. G. G. Amorim ◽  
M. C. B. Fernandes ◽  
F. C. Khanna ◽  
A. E. Santana ◽  
J. D. M. Vianna
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Basic Element ◽  
Space Representation ◽  
Many Body ◽  
Many Body Systems ◽  
The Green Function ◽  
Phase Space Representation

Using elements of symmetry, as gauge invariance, many aspects of a Schrödinger equation in phase space are analyzed. The number (Fock space) representation is constructed in phase space and the Green function, directly associated with the Wigner function, is introduced as a basic element of perturbative procedure. This phase space representation is applied to the Landau problem and the Liouville potential.

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