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Homology of Lie algebra of supersymmetries
Lie algebra supersymmetries
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2010/12/24
We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare algebra. We discuss in detail the calculation in dimensions D=10 and D=6. Our methods can be a...
Newtonian Gravity and the Bargmann Algebra
Newtonian Gravity the Bargmann Algebra
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2010/12/23
We show how the Newton-Cartan formulation of Newtonian gravity can be obtained from gauging the Bargmann algebra, i.e., the centrally extended Galilean algebra. In this gauging procedure several curva...
Dual Kappa Poincare Algebra
Lorentz Poincare and phase space algebras DSR kappa Poincare algebra
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2010/12/21
We show a different modification of Poincare algebra that also preserves the Lorentz algebra. The change begins with how boosts affect space-time in a way similar to how boosts affect the momenta in k...
The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach
Gelfand spectrum noncommutative C*-algebra topos-theoretic approach
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2010/11/11
We compare two influential ways of defining a generalized notion of space. The first, inspired by Gelfand duality, states that the category of 'noncommutative spaces' is the opposite of the category o...
Extending PT symmetry from Heisenberg algebra to E2 algebra
Extending PT symmetry Heisenberg algebra E2 algebra
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2010/10/27
The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u; J] = iv, [v; J] = iu, [u; v] = 0. We can construct the Hamiltonian H = J2 +gu, where g is a real p...
Abelian subalgebras and the Jordan structure of a von Neumann algebra
von Neumann algebra Jordan structure abelian subalgebra orthomodular lattice
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2010/10/27
For von Neumann algebrasM,N without type I2 summands, we show that for an orderisomorphism
f : AbSub M → AbSub N between the posets of abelian von Neumann-subalgebras of M and N, there is a unique Jo...
On the regularization of the constraints algebra of Quantum Gravity in 2+1 dimensions with non-vanishing cosmological constant
Quantum Gravity cosmological constant 2+1 dimensions
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2010/3/18
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usu...
Poincare algebra realized in Hamiltonian formalism of the Relativistic Theory of Gravitation
Relativistic Theory of Gravitation Hamiltonian formalism
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2010/3/17
We obtain the Poincare group generators by proper choice of arbitrary functions present in the Relativistic Theory of Gravitation (RTG) Hamiltonian. Their Dirac brackets give the Poincare algebra in a...
Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics
Cliff ord algebra supersymmetric quantum mechanics deformation quantization Wigner functions Jaynes-Cummings models
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2010/4/13
In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal sta...
Semi-Simple Extension of the (Super) Poincaré Algebra
Semi-Simple Extension dimensional Poincaré algebra Semi-Simple Tensor Extension
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2009/9/4
A semi-simple tensor extension of the Poincaré algebra is proposed for the arbitrary dimensions D. It is established that this extension is a direct sum of the D-dimensional Lorentz algebra so(D−...
Overview of the structural unification of quantum mechanics and relativity using the algebra of quantions
structural unification quantum mechanics relativity the algebra of quantions
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2010/4/7
The purpose of this contribution is to provide an introduction for a general physics audience to the recent results of Emile Grgin that unifies quantum mechanics and relativity into the same mathemati...
Classical and Quantum Mechanics from the universal Poisson-Rinehart algebra of a manifold
Lie-Rinehart algebras Poisson algebras quantization
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2010/4/8
The Lie and module (Rinehart) algebraic structure of vector fields of compact support over C infinity functions on a (connected) manifold M define a unique universal non-commutative Poisson * algebra....
Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra
Coherent states displaced number states Laguerre polynomial states su(1,1) Lie algebra
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2010/10/13
The ladder operator formalism of a general quantum state for su(1,1)ie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Perelomov’s cohe...
Nonlinear Two-Mode Squeezed Vacuum States as Realization of SU(1,1) Lie Algebra
Non-classical field states two-mode squeezed vacuum states nonlinear two-mode coherent states nonlinear pair coherent states squeezing two-mode SU(1,1) lie algebra coherent states
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2010/4/9
Nonlinear extensions of the two-mode squeezed vacuum states (NTMSVS's) are constructed and special cases of these states are discussed. We have constructed the NTMSVS's realization of SU(1,1) Lie alge...
Exact Solutions of Two Coupled Harmonic Oscillators Related
to the Sp(4,R) Lie Algebra
coupled harmonic oscillators Sp(4 R) Lie algebra vector coherent states
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2007/8/15
2001Vol.35No.6pp.661-664DOI:
Exact Solutions of Two Coupled Harmonic Oscillators Related
to the Sp(4,R) Lie Algebra
PAN Feng and DAI Lian-Rong
Department of Physics, Lia...