A C*-algebra approach to the Schwinger model

If cutoffs are introduced then existing results in the literature show that the Schwinger model is dynamically equivalent to a boson model with quadratic Hamiltonian. However, the process of quantising the Schwinger model destroys local gauge invariance. Gauge invariance is restored by the addition of a counterterm, which may be seen as a finite renormalisation, whereupon the Schwinger model becomes dynamically equivalent to a linear boson gauge theory. This linear model is exactly soluble. We find that different treatments of the supplementary (i.e. Lorentz) condition lead to boson models with rather different properties. We choose one model and construct, from the gauge invariant subalgebra, a class of inequivalent charge sectors. We construct sectors which coincide with those found by Lowenstein and Swieca for the Schwinger model. A reconstruction of the Hilbert space on which the Schwinger model exists is described and fermion operators on this space are defined.     

Renormalization of singular potentials and power counting

We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r² potential perturbed by a 1/r⁴ correction. The power-counting rule, an important ingredient of effective theory, is established by seeking the minimum set of short-range counterterms that renormalize the scattering amplitude. We show that leading-order counterterms are needed in all partial waves where the potential overcomes the centrifugal barrier, and that the additional counterterms at next-to-leading order are the ones expected on the basis of dimensional analysis.     

Chern–Simons theory with vector fermion matter

We study three-dimensional conformal field theories described by U(N) Chern?CSimons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger?CDyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on ?² as a function of the ??t?Hooft coupling ??=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |??|=1; the conformal theory does not exist for |??|>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W _?? algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.     

Batalin-Tyutin quantization of the chiral Schwinger model

We quantize the chiral Schwinger model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first-class constraints and the desired involutive Hamiltonian, which naturally generates all secondary constraints. Fora>1, this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess-Zumino terms, while fora=1 the corresponding Lagrangian has the additional new type of the Wess-Zumino terms, which are irrelevant to the gauge symmetry.     

Determination of Phase Space Spectra of the Generalized Chiral Schwinger model with the Lorentz invariant Mass like Term for the Choice a − r2 = 0

We have considered the generalized version of chiral schwinger model with the Lorentz covariant masslike term for gauge field with the choice a ? r² =?0. We carry out the quantization by the canonical Dirac method of both the gauge-invariant and non-invariant version of this model to determine the phase space structure. Therefore we have shown that the gauge invariant theory has the same physical spectrum as that of the original gauge noninvariant formulation.

     

A theorem on the existence of dyon solutions

We prove the existence of finite energy dyon solutions to Yang-Mills-Higgs equations satisfying the Julia-Zee ansatz, and the generalization to SU(N) gauge groups. This rigorously establishes the existence of a model for the particles having electric and magnetic charge conjectured by Schwinger. We also prove that the solutions are real analytic on (0, ∞) and C^∞ at r = 0. To establish our result we prove a new abstract theorem that allows one to study singular constrained minimization problems without the introduction of Lagrange multipliers.     

Construction ofYM 4 with an infrared cutoff

We provide the basis for a rigorous construction of the Schwinger functions of the pure SU(2) Yang-Mills field theory in four dimensions (in the trivial topological sector) with a fixed infrared cutoff but no ultraviolet cutoff, in a regularized axial gauge. The construction exploits the positivity of the axial gauge at large field. For small fields, a different gauge, more suited to perturbative computations is used; this gauge and the corresponding propagator depends on large background fields of lower momenta. The crucial point is to control (in a non-perturbative way) the combined effect of the functional integrals over small field regions associated to a large background field and of the counterterms which restore the gauge invariance broken by the cutoff. We prove that this combined effect is stabilizing if we use cutoffs of a certain type in momentum space. We check the validity of the construction by showing that Slavnov identities (which express infinitesimal gauge invariance) do hold non-perturbatively.     

The Schwinger model: A view from the temporal gauge

We present a new operator solution of the Schwinger model, i.e., of massless quantum electrodynamics in 1 + 1 dimensions in the temporal gauge A⁰ = 0. This gauge is well-suited for the treatment of static external charges. The energy functional reflects the immediate onset of pair creation of massless fermions. We show that every point charge is screened completely by a Yukawa-like polarization charge cloud of radius $\text{π}\text{e}$, e the coupling constant.     

One Fermion-Loop Correction and Supersymmetry in the Heterotic String Theory

(2, 0) world-sheet supersymmetry is shown to be one of the necessary conditions for space-time supersymmetry in most cases. Special care is taken to study the cancellation of local Lorentz and gauge anomalies caused by one fermion-loop..My computation shows that local counterterms which simultaneously restore local Lorentz and gauge invariance of the sigma model do not satisfy the criteria of (2, 0) supersymmetry. But local counterterms and the non-local part of one loop effective action are together invariant under the (2, 0) supersymmetry transformation.     

Quantization of the anomalous,chiral, Schwinger model

We implement the recent proposal of Faddeev [6] and present a quantization of the anomalous, chiral, Schwinger model. We carry out a Schrödinger representation, hamiltonian formulation quantization, on a circle. We expose the structure of the fermionic Hilbert bundle as a functional of the background gauge fields. We find that, although a unitary and consistent quantum field theory is obtained, Lorentz invariance is lost.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Extended Einstein–Cartan theory à la Diakonov: The field equations

Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincaré gauge theory (PGT). Thus, the gravitational field variables are the orthonormal coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein–Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonov?s model the coframe is eliminated by expressing it in terms of the primordial spinor. We derive the corresponding field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection, but keeping local Lorentz covariance intact. Then, if we drop the Einstein–Cartan term in the Lagrangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.     

Hamiltonian quantization of the non-anomalous generalized Schwinger model

We quantize a generalized version of the Schwinger model, where the two chiral sectors couples with different strengths to theU(1) gauge field. Starting from a theory which includes a generalized Wess-Zumino term, we obtain the equal time commutation relation for physical fields, both the singular and non-singular cases are considered. The photon propagators are also computed in their gauge dependent and invariant versions.     

Fields nonlocal in clifford space

A previously proposed field theory is quantized. The theory contains a parameter having the character of an elementary length. We fix the value of this parameter by scaling it to the weak interaction strength. It is shown that this way negative metric states are confined to a region of the order 10^?15 cm. The resulting quantum theory of interacting fields is Lorentz and gauge invariant, has a unitaryS-matrix, and is convergent.     

Spinor theory of general relativity without elementary gravitons

We propose a generally covariant and locally Lorentz invariant theory of a Majorana spinor field ψ_μ^α. Our theory has no elementary spin-2 quanta, but does reproduce Einstein's general relativity as a classical solution. We compare this situation to the possibility of finding classical monopoles in a gauge theory, even though no such elementary object is introduced at the outset.     

Remark on the consistent gauge anomaly in supersymmetric theories

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d^abc=trT^a{T^b,T^c}, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess–Zumino consistency condition.     

Chiral Schwinger model with new regularization

A recently proposed version of the chiral Schwinger model is studied in detail in this paper. It is shown that a suitable Pauli-Villars regularization can be devised to reproduce the bosonized form of the effective action that was earlier written down. It is then shown how this anomalous gauge theory can be made gauge invariant by the introduction of a Wess-Zumino field. The equations of motion of this theory are explicitly solved in Lorentz covariant gauges. Finally, the operator solution of the fermionic form of the theory is constructed.