119351968
CPT/Lorentz Invariance Violation and Quantum Field Theory
Departamento de Fisica, Universidad de Santiago de ChileCasilla 307, Santiago 2, ChileE-mail: fmendez@lauca.usach.clAnalogies between the noncommutative harmonic oscillator and noncommutative ﬁelds are ana-lyzed. Following this analogywe construct examples of quantum ﬁelds theories with explicit CPTand Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation arealso discussed.Fifth International Conference on Mathematical Methods in Physics — IC2006April 24-28 2006Centro Brasilerio de Pesquisas Fisicas, Rio de Janeiro, Brazil
123610301
The hamiltonian structures of the KP hierarchy
Abstract We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra.
18810830
The sTB-B hierarchy
Abstract We construct a new supersymmetric two boson (sTB-B) hierarchy and study its properties. We derive the conserved quantities and the Hamiltonian structures (proving the Jacobi identity) for the system. We show how this system gives the sKdV-B equation and its Hamiltonian structures upon appropriate reduction. We also describe the zero curvature formulation of this hierarchy both in the superspace as well as in components.
120503298
Systematic expansion for compact QED near weak coupling
39204644
Thermal Operator and Cutting Rules at Finite Temperature and Chemical Potential
In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal operator. We give an alternative algebraic proof of the largest time equation which brings out the underlying physics of such a relation. As an application of the cutting description, we calculate the imaginary part of the one-loop retarded self-energy at zero/finite temperature and finite chemical potential and show how this description can be used to calculate the dispersion relation as well as the full physical self-energy of thermal particles.
119380448
DYNAMICAL SUPERSYMMETRY
We show, in a simple quantum mechanical model, how a theory can become supersymmetric in the presence of interactions even when the free theory is not. This dynamical generation of supersymmetry relaxes the condition on the equality of masses of the superpartners which would be of phenomenological interest.
119529576
Quantization in a general light-front frame
In this paper, we study the question of quantization of quantum field theories in a general light-front frame. We quantize scalar and fermion as well as gauge field theories in a systematic manner carrying out the Hamiltonian analysis carefully. The decomposition of the fields into positive and negative frequency terms needs to be done carefully after which we show that the (anti) commutation relations for the quantum operators become frame independent. The frame dependence is completely contained in the functions multiplying these operators in the field decomposition. We derive the propagators from the vacuum expectation values of the time ordered products of the fields.
118546083
Finite temperature effective actions
Abstract We present, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature, which can be used to determine the finite temperature effective action for the system. As applications, we determine the complete one loop finite temperature effective actions for ( 0 + 1 )-dimensional QED as well as the Schwinger model. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories.
15661741
Propagators with the Mandelstam-Leibbrandt prescription in the light-cone gauge
We show that the Feynman propagator in the light-cone gauge with the Mandelstam-Leibbrandt prescription has a logarithmic growth for large n-tilde{center_dot}x which is related to the presence of a residual gauge invariance. Furthermore, we show that the retarded propagator for the n-tilde{center_dot}A component of the gauge field develops a coordinate dependent mass. We argue that this feature is unphysical and may be eliminated by fixing the residual gauge degrees of freedom.
30161988
Physics of quantum relativity through a linear realization
The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie algebra, we implement explicitly a simple linear realization of the relativity symmetry, and explore systematically the resulting physical interpretations. Some suggestions we make may sound radical, but are arguably natural within the context of our formulation. Our work may provide a new perspective on the subject matter, complementary to the previous approach(es), and may lead to a better understanding of the physics.
17610218
A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy
Abstract In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.