2,029 research outputs found
On the Symmetries of Hamiltonian Systems
In this paper we show how the well-know local symmetries of Lagrangeans
systems, and in particular the diffeomorphism invariance, emerge in the
Hamiltonian formulation. We show that only the constraints which are linear in
the momenta generate transformations which correspond to symmetries of the
corresponding Lagrangean system. The nonlinear constraints (which we have, for
instance, in gravity, supergravity and string theory) rather generate the
dynamics of the corresponding Lagrangean system. Only in a very special
combination with "trivial" transformations proportional to the equations of
motion do they lead to symmetry transformations. We reveal the importance of
these special "trivial" transformations for the interconnection theorems which
relate the symmetries of a system with its dynamics. We prove these theorems
for general Hamiltonian systems. We apply the developed formalism to concrete
physically relevant systems and in particular those which are diffeomorphism
invariant. The connection between the parameters of the symmetry
transformations in the Hamiltonian- and Lagrangean formalisms is found. The
possible applications of our results are discussed.Comment: 44 page
Running surface couplings
We discuss the renormalization group improved effective action and running
surface couplings in curved spacetime with boundary. Using scalar
self-interacting theory as an example, we study the influence of the boundary
effects to effective equations of motion in spherical cap and the relevance of
surface running couplings to quantum cosmology and symmetry breaking
phenomenon. Running surface couplings in the asymptotically free SU(2) gauge
theory are found.Comment: 11 pages, Latex fil
Alternating current losses in superconducting coils
Report examines relationship between coil loss and frequency and heat loss in coil as a function of the magnetic field H. Information is of value to manufacturers of superconducting magnets, motors and generators
Phases of supersymmetric O(N) theories
We perform a global renormalization group study of O(N) symmetric Wess-Zumino
theories and their phases in three euclidean dimensions. At infinite N the
theory is solved exactly. The phases and phase transitions are worked out for
finite and infinite short-distance cutoffs. A distinctive new feature arises at
strong coupling, where the effective superfield potential becomes multi-valued,
signalled by divergences in the fermion-boson interaction. Our findings resolve
the long-standing puzzle about the occurrence of degenerate O(N) symmetric
phases. At finite N, we find a strongly-coupled fixed point in the local
potential approximation and explain its impact on the phase transition. We also
examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon,
and relate our findings with the spontaneous breaking of supersymmetry in other
models.Comment: 23 pages, 18 figure
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