Search results for "quantization"
showing 10 items of 253 documents
DEFORMATION QUANTIZATION OF COADJOINT ORBITS
2000
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
Supersymmetry in non commutative superspaces
2003
Non commutative superspaces can be introduced as the Moyal-Weyl quantization of a Poisson bracket for classical superfields. Different deformations are studied corresponding to constant background fields in string theory. Supersymmetric and non supersymmetric deformations can be defined, depending on the differential operators used to define the Poisson bracket. Some examples of deformed, 4 dimensional lagrangians are given. For extended superspace (N>1), some new deformations can be defined, with no analogue in the N=1 case.
Cohomological analysis of gauged-fixed gauge theories
1999
The relation between the gauge-invariant local BRST cohomology involving the antifields and the gauge-fixed BRST cohomology is clarified. It is shown in particular that the cocycle conditions become equivalent once it is imposed, on the gauge-fixed side, that the BRST cocycles should yield deformations that preserve the nilpotency of the (gauge-fixed) BRST differential. This shows that the restrictions imposed on local counterterms by the Quantum Noether condition in the Epstein--Glaser construction of gauge theories are equivalent to the restrictions imposed by BRST invariance on local counterterms in the standard Lagrangian approach.
PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE
2012
Motivated by the Goldbach conjecture in Number Theory and the abelian bosonization mechanism on a cylindrical two-dimensional spacetime we study the reconstruction of a real scalar field as a product of two real fermion (so-called \textit{prime}) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators $b_{p}^{\dag}$ --labeled by prime numbers $p$-- acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allow us to prove that the theory is not renormalizabl…
Spinor moving frame, M0-brane covariant BRST quantization and intrinsic complexity of the pure spinor approach
2007
To exhibit the possible origin of the inner complexity of the Berkovits's pure spinor approach, we consider the covariant BRST quantization of the D=11 massless superparticle (M0-brane) in its spinor moving frame or twistor-like Lorentz harmonics formulation. The presence of additional twistor-like variables (spinor harmonics) allows us to separate covariantly the first and the second class constraints. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints algebra, the dynamical system is described by the cohomology of a simple BRST charge associated to the d=1, n=16 supersymmetry algebra. The calculation of …
Free field realization of cylindrically symmetric Einstein gravity
1998
Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.
D=11massless superparticle covariant quantization, pure spinor BRST charge and hidden symmetries
2007
We consider the covariant quantization of the D=11 massless superparticle (M0-brane) in the spinor moving frame or twistor-like Lorentz harmonics formulation. The action involves the set of 16 constrained 32 component Majorana spinors, the spinor Lorentz harmonics parametrizing (as homogeneous coordinates, modulo gauge symmetries) the celestial sphere S9. There presence allows us to separate covariantly the first and the second class constraints of the model. After taking into account the second class constraints by means of Dirac brackets and after further reducing the first class constraints algebra, the system is described in terms of a simple BRST charge associated to the d=1, n=16 supe…
On the physical contents of q-deformed Minkowski spaces
1994
Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to contain unusual features. At the same time, it is argued that the formulation of an associated $q$-deformed field theory is fraught with serious difficulties.
Deterministic Quantization by Dynamical Boundary Conditions
2010
We propose an unexplored quantization method. It is based on the assumption of dynamical space-time intrinsic periodicities for relativistic fields, which in turn can be regarded as dual to extra-dimensional fields. As a consequence we obtain a unified and consistent interpretation of Special Relativity and Quantum Mechanics in terms of Deterministic Geometrodynamics.
Quantum Field Theory on a Discrete Space and Noncommutative Geometry
2001
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied without being spoiled by technical complications due to the absence of divergencies.