758 research outputs found
Extremes of multidimensional Gaussian processes
This paper considers extreme values attained by a centered, multidimensional Gaussian process t) = (X_1(t), ..., X_n(t)) minus drift d(t) = (d_1(t), ..., d_n(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of the logarithm of the probability that for some t in T, we have that (for all i = 1, ..., n) X_i(t) - d_i(t) > q_i u, for positive thresholds q_i > 0 and u large. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional case. A number of examples illustrate the theory
Projective representation of k-Galilei group
The projective representations of k-Galilei group G_k are found by
contracting the relevant representations of k-Poincare group. The projective
multiplier is found. It is shown that it is not possible to replace the
projective representations of G_k by vector representations of some its
extension.Comment: 15 pages Latex fil
Velocity of particles in Doubly Special Relativity
Doubly Special Relativity (DSR) is a class of theories of relativistic motion
with two observer-independent scales. We investigate the velocity of particles
in DSR, defining velocity as the Poisson bracket of position with the
appropriate hamiltonian, taking care of the non-trivial structure of the DSR
phase space. We find the general expression for four-velocity, and we show
further that the three-velocity of massless particles equals 1 for all DSR
theories. The relation between the boost parameter and velocity is also
clarified.Comment: 12 page
Scalar field theory on -Minkowski space-time and Doubly Special Relativity
In this paper we recall the construction of scalar field action on
-Minkowski space-time and investigate its properties. In particular we
show how the co-product of -Poincar\'e algebra of symmetries arises
from the analysis of the symmetries of the action, expressed in terms of
Fourier transformed fields. We also derive the action on commuting space-time,
equivalent to the original one. Adding the self-interaction term we
investigate the modified conservation laws. We show that the local interactions
on -Minkowski space-time give rise to 6 inequivalent ways in which
energy and momentum can be conserved at four-point vertex. We discuss the
relevance of these results for Doubly Special Relativity.Comment: 17 pages; some editing done, final version to be published in Int. J.
Mod. Phys.
Impossibility of spontaneously breaking local symmetries and the sign problem
Elitzur's theorem stating the impossibility of spontaneous breaking of local
symmetries in a gauge theory is reexamined. The existing proofs of this theorem
rely on gauge invariance as well as positivity of the weight in the Euclidean
partition function. We examine the validity of Elitzur's theorem in gauge
theories for which the Euclidean measure of the partition function is not
positive definite. We find that Elitzur's theorem does not follow from gauge
invariance alone. We formulate a general criterion under which spontaneous
breaking of local symmetries in a gauge theory is excluded. Finally we
illustrate the results in an exactly solvable two dimensional abelian gauge
theory.Comment: Latex 6 page
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