scholarly journals Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

2015 ◽  
Vol 30 (20) ◽  
pp. 1550115 ◽  
Author(s):  
D. Shukla ◽  
T. Bhanja ◽  
R. P. Malik
Keyword(s):  
Present Method ◽  
Hodge Theory ◽  
Rigid Rotor ◽  
Normal Ordering ◽  
Creation And Annihilation Operators ◽  
Basic Concepts ◽  
Definition Of ◽  
Continuous Symmetries ◽  
Internal Symmetries ◽  
Theory Lead

We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one [Formula: see text]-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

Realization of Lie algebras and superalgebras in terms of creation and annihilation operators: I

2000 ◽  
Vol 124 (2) ◽  
pp. 1048-1058 ◽  
Author(s):  
Č. Burdík ◽  
P. Grozman ◽  
D. Leites ◽  
A. Sergeev
Keyword(s):  
Lie Algebras ◽  
Creation And Annihilation Operators

Quantum Many-Particle Systems and Second Quantization

2019 ◽  
pp. 5-44
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Quantum Mechanics ◽  
Particle Physics ◽  
Mathematical Formulation ◽  
Particle Systems ◽  
Quantum Field ◽  
Second Quantization ◽  
Creation And Annihilation Operators ◽  
Quantum Matter ◽  
Interacting Systems ◽  
The Many

Chapter 2 provides a review of pertinent aspects of the quantum mechanics of systems composed of many particles. It focuses on the foundations of quantum many-particle physics, the many-particle Hilbert spaces to describe large assemblies of interacting systems composed of Bosons or Fermions, which lead to the versatile formalism of second quantization as a convenient and eminently practical language ubiquitous in the mathematical formulation of the theory of many-particle systems of quantum matter. The main objects in which the formalism of second quantization is expressed are the Bosonic or Fermionic creation and annihilation operators that become, in the position basis, the quantum field operators.

A q-deformed particle algebra with a unique d-dimensional representation

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Şeyda Tekin ◽  
Metin Arik
Keyword(s):  
Single Pair ◽  
Dimensional Representation ◽  
Creation And Annihilation Operators ◽  
Quantum Numbers

AbstractWe present an algebra generated by a single pair of creation and annihilation operators b and b*. We prove that the algebra has a unique d-dimensional representation. Physically this algebra corresponds to a system where there are at most d − 1 particles in a state with otherwise same quantum numbers.

COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA

2009 ◽  
Vol 24 (25) ◽  
pp. 2039-2051 ◽  
Author(s):  
H. FAKHRI ◽  
B. MOJAVERI ◽  
A. DEHGHANI
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Heisenberg Algebra ◽  
Creation And Annihilation Operators ◽  
Number Of Generators ◽  
Simple Harmonic Oscillator

We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with [Formula: see text] and [Formula: see text] symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are [Formula: see text]-pseudo-Hermiticity and [Formula: see text]-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

New Creation and Annihilation Operators in Phase Space

1978 ◽  
Vol 45 (1) ◽  
pp. 336-342 ◽  
Author(s):  
A. Jannussis ◽  
N. Patargias ◽  
G. Brodimas
Keyword(s):  
Phase Space ◽  
Creation And Annihilation Operators ◽  
New Creation
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