2,425 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
Supersymmetry breaking as a quantum phase transition
We explore supersymmetry breaking in the light of a rich fixed-point
structure of two-dimensional supersymmetric Wess-Zumino models with one
supercharge using the functional renormalization group (RG). We relate the
dynamical breaking of supersymmetry to an RG relevant control parameter of the
superpotential which is a common relevant direction of all fixed points of the
system. Supersymmetry breaking can thus be understood as a quantum phase
transition analogously to similar transitions in correlated fermion systems.
Supersymmetry gives rise to a new superscaling relation between the critical
exponent associated with the control parameter and the anomalous dimension of
the field -- a scaling relation which is not known in standard spin systems.Comment: 5 pages, 2 figures, discussion of results extended, version to appear
as a Rapid Communication in Phys. Rev.
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