arXiv subjects

H. Pfeiffer

Publications and source records attributed to H. Pfeiffer.

7 recordsLinked to original sources

arXiv2008

Topological Higher Gauge Theory - from BF to BFCG theory

We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature: the SigmaPhiEA-model of 3-dimensional gravity coupled to topological matter, and also a 4-dimensional model of BF-theory coupled to topological matter.

hep-th↗

arXiv2000

Symplectic and orthogonal Lie algebra technology for bosonic and fermionic oscillator models of integrable systems

To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper develops a presentation of these Lie algebras convenient for the context, and derives many properties of the matrices of their defining representations and of the ad-invariant tensors that enter their multiplication laws. Metaplectic-type representations of sp(2n) and so(N) on bosonic and on fermionic Fock spaces respectively are constructed. Concise general expressions (see (5.2) and (5.5) below) for their L-operators are obtained, and used to derive simple formulas for the T operators of the rational RTT algebra of the associated integral systems, thereby enabling their efficient treatment by means of the algebraic Bethe ansatz.

math-ph↗

arXiv1999

Scaling of magnetic monopoles in the pure compact QED

In the pure U(1) lattice gauge theory with the Villain action we find that the monopole mass in the Coulomb phase and the monopole condensate in the confinement phase scale according to simple power laws. This holds outside the coupling region in which on finite toroidal lattices the metastability phenomena occur. A natural explanation of the observed accuracy of the scaling behaviour would be the second order of the phase transition between both phases in the general space of couplings not far away from the Villain action.

hep-lat↗

arXiv1999

On characteristic equations, trace identities and Casimir operators of simple Lie algebras

Two approaches are developed to exploit, for simple complex or compact real Lie algebras g, the information that stems from the characteristic equations of representation matrices and Casimir operators. These approaches are selected so as to be viable not only for `small' Lie algebras and suitable for treatment by computer algebra. A very large body of new results emerges in the forms, a) of identities of a tensorial nature, involving structure constants etc. of g, b) of trace identities for powers of matrices of the adjoint and defining representations of g, c) of expressions of non-primitive Casimir operators of g in terms of primitive ones. The methods are sufficiently tractable to allow not only explicit proof by hand of the non-primitive nature of the quartic Casimir of g2, f4, e6, but also e.g. of that of the tenth order Casimir of f4.

math-ph↗

arXiv1999

Scaling analysis of the magnetic monopole mass and condensate in the pure U(1) lattice gauge theory

We observe the power law scaling behavior of the monopole mass and condensate in the pure compact U(1) gauge theory with the Villain action. In the Coulomb phase the monopole mass scales with the exponent ν_m=0.49(4). In the confinement phase the behavior of the monopole condensate is described with remarkable accuracy by the exponent β_{exp}=0.197(3). Possible implications of these phenomena for a construction of a strongly coupled continuum U(1) gauge theory are discussed.

hep-lat↗

arXiv1998

Study of the order of the phase transition in pure U(1) gauge theory with Villain action

We address the question of the order of the deconfinement phase transition of four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory dual to the Villain action on toroidal lattices up to lattice sizes of 28^4 give results consistent with both, a vanishing and a nonvanishing discontinuity in the thermodynamic limit. A decision on the order of the phase transition requires still larger lattice sizes.

hep-lat↗

arXiv1998

Universality of the gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

We continue numerical studies of the spectrum of the pure U(1) lattice gauge theory in the confinement phase, initiated in our previous work. Using the extended Wilson action $ S = -\sum_P [β\cos(Θ_P) + γ\cos(2Θ_P)] $ we address the question of universality of the phase transition line in the ($β,γ$) plane between the confinement and the Coulomb phases. Our present results at $γ= -0.5$ for the gauge-ball spectrum are fully consistent with the previous results obtained at $γ= -0.2$. Again, two different correlation length exponents, $ν_{ng} = 0.35(3)$ and $ν_{g} = 0.49(7)$, are obtained in different channels. We also confirm the stability of the values of these exponents with respect to the variation of the distance from the critical point at which they are determined. These results further demonstrate universal critical behaviour of the model at least up to correlation lengths of 4 lattice spacings when the phase transition is approached in some interval at $γ\leq -0.2$.

hep-lat↗