Matter fields in the Lagrangian loop representation: scalar QED

Aroca, J. M.; Baig, M.; Fort, Hugo; Siri, R.

doi:10.1016/0370-2693(95)01361-x

Cited by 5 publications

(11 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[9], the loop action (27) corresponding to Villain form of U (1) model was considered. The extension of the Lagrangian loop description in such a way to include matter fields was also simulated [10]. The lattice path integral of U (1)-Higgs model is expressed as a sum over closed as much as open surfaces.…”

Section: Discussionmentioning

confidence: 99%

“…A path integral loop formulation will allow to employ the more powerful statistical computation techniques. Gauge invariant actions corresponding to the Villain form of the U(1) model were proposed recently [9] and generalized to include matter fields [10].…”

Section: Introductionmentioning

confidence: 99%

“…Simple thermal cycles showed the presence of a phase transition in the neighborhood of β V = 0.639. In the case of of U(1)-Higgs model, the β-γ phase diagram was mapped out [10]. In both models, by virtue of the gauge invariance of this description, the equilibrium configurations were reached faster than with the ordinary gauge-variant descriptions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Path integral for the loop representation of lattice gauge theories

1996

Self Cite

View full text Add to dashboard Cite

We show how the Hamiltonian lattice loop representation can be cast straightforwardly in the path integral formalism. The procedure is general for any gauge theory. Here we present in detail the simplest case: pure compact QED. The lattice loop path integral approach allows us to knit together the power of statistical algorithms with the transparency of the gauge-invariant loop description. The results produced by numerical simulations with the loop classical action for different lattice models are discussed. We also analyze the lattice path integral in terms of loops for the non-Abelian theory.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Path integral for the loop representation of lattice gauge theories

1996

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is the Lagrangian counterpart of the former introduced Hamiltonian loop representation [14,15]. Although the non-canonical nature of the loop algebra had made elusive this Lagrangian formulation, in a previous set of papers [16,17] a procedure to cast loops into the so-called world-sheet formulation was introduced.…”

Section: Introductionmentioning

confidence: 99%

Finite size analysis of the U(1) phase transition using the world-sheet formulation

1999

Self Cite

View full text Add to dashboard Cite

We present a high statistics analysis of the pure gauge compact U(1) lattice theory using the the world−sheet or Lagrangian loop representation. We have applied a simulation method that deals directly with (gauge invariant) integer variables on plaquettes. As a result we get a significant amelioration of the simulation that allows to work with large lattices avoiding the metaestability problems that appear using the standard Wilson formulation.

show abstract

“…Recently a Lagrangian approach in terms of loops has been developed for the U(1) model [5], and generalized to include matter fields [6]. The resulting action is proportional to the quadratic area of the loop worldsheet.…”

Section: Introductionmentioning

confidence: 99%

Path integral loop representation of 2+1 lattice non-Abelian gauge theories

Aroca

Fort²,

Gambini

1998

Phys. Rev. D

View full text Add to dashboard Cite

A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The corresponding path integral for SU(2) lattice gauge theory is expressed as a sum over colored surfaces, i.e. only involving the jp attached to the lattice plaquettes. This surfaces may be interpreted as the world sheets of the spin networks In 2+1 dimensions, this can be accomplished by working in a lattice dual to a tetrahedral lattice constructed on a face centered cubic Bravais lattice. On such a lattice, the integral of gauge variables over boundaries or singular lines -which now always bound three coloured surfaces -only contributes when four singular lines intersect at one vertex and can be explicitly computed producing a 6-j or Racah symbol. We performed a strong coupling expansion for the free energy. The convergence of the series expansions is quite different from the series expansions which were performed in ordinary cubic lattices. In the case of ordinary cubic lattices the strong coupling expansions up to the considered truncation number of plaquettes have the great majority of their coefficients positive, while in our case we have almost equal number of contributions with both signs. Finally, it is discused the connection in the naive coupling limit between this action and that of the B-F topological field theory and also with the pure gravity action.

show abstract

Matter fields in the Lagrangian loop representation: scalar QED

Cited by 5 publications

References 23 publications

Path integral for the loop representation of lattice gauge theories

Path integral for the loop representation of lattice gauge theories

Finite size analysis of the U(1) phase transition using the world-sheet formulation

Path integral loop representation of 2+1 lattice non-Abelian gauge theories

Contact Info

Product

Resources

About