Vacuum structure and the fermion-boson transformation (original) (raw)
Dressed fermions, modular transformations and bosonization in the compactified Schwinger model
Journal of Physics A: Mathematical and Theoretical, 2012
The celebrated exactly solvable "Schwinger" model, namely massless twodimensional QED, is revisited. The solution presented here emphasizes the nonperturbative relevance of the topological sector through large gauge transformations whose role is made manifest by compactifying space into a circle. Eventually the well-known non-perturbative features and solution of the model are recovered in the massless case. However the fermion mass term is shown to play a subtle role in order to achieve a physical quantization that accounts for gauge invariance under both small and large gauge symmetries. Quantization of the system follows Dirac's approach in an explicitly gauge invariant way that avoids any gauge fixing procedure.
The structure of the gauge theory vacuum
Physics Letters B, 1976
The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.
Geometry, Topology and Quantum Field Theory
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The Schrödinger Representation for Fermions and a Local Expansion of the Schwinger Model
International Journal of Modern Physics A, 2000
We discuss the functional representation of fermions, and obtain exact expressions for wave-functionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations, the vacuum wave-functional does not simplify at large distances, but it may be reconstructed as a large time limit of the Schrödinger functional, which has an expansion in local terms. The functional Schrödinger equation reduces to a set of algebraic equations for the coefficients of these terms. These ideas generalize to a numerical approach to QCD in higher dimensions.
Gauge invariant reformulation and BRST quantization of the nonconfining Schwinger model
A new generalization of the vector Schwinger model is considered where gauge symmetry is broken at the quantum mechanical level. By proper extension of the phase space this broken symmetry has been restored. Also an equivalent first class theory is reformulated in the actual phase space using Mitra and Rajaraman's prescription [8, 9]. A BRST invariant effective action is also formulated. The new dynamical fields introduced, turn into Wess-Zumino scalar.
A Condensed Matter Interpretation of SM Fermions and Gauge Fields
We present the bundle (Aff(3)⊗C⊗ )(R 3 ), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (C ⊗ )(R 3 ) describes an electroweak doublet. The Dirac equation has a doublerfree staggered spatial discretization on the lattice space (Aff(3) ⊗ C)(Z 3 ). This space allows a simple physical interpretation as a phase space of a lattice of cells.
Instantons and the infrared behavior of the fermion propagator in the Schwinger model
The European Physical Journal C, 2008
Fermion propagator of the Schwinger Model is revisited from the point of view of its infrared behavior. The values of anomalous dimensions are found in arbitrary covariant gauge and in all contributing instanton sectors. In the case of a gauge invariant, but path dependent propagator, the exponential dependence, instead of power law one, is established for the special case when the path is a straight line. The leading behavior is almost identical in any sector, differing only by the slowly varying, algebraic prefactors. The other kind of the gauge invariant function, which is the amplitude of the dressed Dirac fermions, may be reduced, by the appropriate choice of the dressing, to the gauge variant one, if Landau gauge is imposed.
Gauge-Field Theory of Particles. II. Fermions
Physical Review D, 1972
We construct classes of Lagrangians which describe families of fermions containing an infinite number of particles. The Lagrangians depend on Rarita-Schwinger fields with k Lorentz indices, k =1, 2, ... , which have bilinear interactions among themselves. These Lagrangians are invariant under gauge transformations of the second kind. The physical states appear as the normal modes of these field theories, and by suitable choices of the masses of the underlying gauge fields, the physical fermions can be made to lie on linearly rising Regge trajectories. The currents have nontrivial diagonal matrix elements, and also have matrix elements between states of different spin. By considering time-ordered products of currents between single-particle states, we are able to construct onand off-mass-shell N-point functions in the narrow-resonance approximation.
Quantum field theories with fermions in the Schrödinger representation
2000
This thesis is concerned with the Schrodinger representation of quantum field theory. We describe techniques for solving the Schrodinger equation which supplement the standard techniques of field theory. Our aim is to develop these to the point where they can readily be used to address problems of current interest. To this end, we study realistic models such as gauge theories coupled to dynamical fermions. For maximal generality we consider particles of all physical spins, in various dimensions, and eventually, curved spacetimes. We begin by considering Gaussian fields, and proceed to a detailed study of the Schwinger model, which is, amongst other things, a useful model for (3+1) dimensional gauge theory. One of the most important developments of recent years is a conjecture by Maldacena which relates supergravity and string/M-theory on anti-de-Sitter spacetimes to conformal field theories on their boundaries. This correspondence has a natural interpretation in the Schrodinger representation, so we solve the Schrodinger equation for fields of arbitrary spin in anti-de-Sitter spacetimes, and use this to investigate the conjectured correspondence. Our main result is to calculate the Weyl anomalies arising from supergravity fields, which, summed over the supermultiplets of type IIB supergravity compactified on AdS^ x 5^ correctly matches the anomaly calculated in the conjecturally dual A/" = 4 SU(N) super-Yang-Mills theory. This is one of the few existing pieces of evidence for Maldacena's conjecture beyond leading order in A'^.
International Journal of Modern Physics A, 2001
By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of...
Annals of Physics, 2002
Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In the QED 2 with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In the anomalous chiral QED 2 with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.
Three topics in the Schwinger model
Nuclear Physics B - Proceedings Supplements, 1998
1. We compare Monte Carlo results with analytic predictions for the fermion condensate, in the massive oneflavour Schwinger model. 2. We illustrate on the Schwinger model how to facilitate transitions between topological sectors by a simple reweighting method. 3. We discuss exact, non-perturbative improvement of the gauge sector.
Topological Structure of the QCD Vacuum Revealed by Overlap Fermions
High Performance Computing in Science and Engineering, Garching/Munich 2009, 2010
Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge and the localization and local chirality of the overlap eigenmodes are reported. The charge distribution is radically different, if a spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is changing from the scale-a charge density (with full lattice resolution) to the ultraviolet filtered charge density. The scale-a density, computed on the Linux cluster of LRZ, has a singular, sign-coherent global structure of co-dimension 1 first described by the Kentucky group. We stress, however, the cluster properties of the UV filtered topological density resembling the instanton picture. The spectral cut-off can be mapped to a bosonic smearing procedure. The UV filtered field strength reveals a high degree of (anti)selfduality at "hot spots" of the action. The fermionic eigenmodes show a high degree of local chirality. The lowest modes are seen to be localized in low-dimensional space-time regions.
Gauga invariant reformulation and BRST quantization of the nonconfining Schwinger model
1995
A new generalization of the vector Schwinger model is considered where gauge symmetry is broken at the quantum mechanical level. By proper extension of the phase space this broken symmetry has been restored. Also an equivalent first class theory is reformulated in the actual phase space using Mitra and Rajaraman’s prescription [8, 9]. A BRST invariant effective action is also formulated. The new dynamical fields introduced, turn into Wess-Zumino scalar. 1 1
The Schwinger Model and the Physical Projector: A Nonperturbative Quantization Without Gauge Fixing
Contemporary Problems in Mathematical Physics - Proceedings of the Second International Workshop, 2002
Based on the physical projector approach, a nonpertubative quantization of the massless Schwinger model is considered which does not require any gauge fixing. The spectrum of physical states, readily identified following a diagonalization of the operator algebra, is that of a massive pseudoscalar field, namely the electric field having acquired a mass proportional to the gauge coupling constant. The physical spectrum need not be identified with confined bound fermion-antifermion pairs, an interpretation which one is otherwise led to given whatever gauge fixing procedure but which is not void of gauge fixing artefacts.
PROGRESS IN PHYSICS Fermions as Topological Objects
2005
A preon-based composite model of the fundamental fermions is discussed, in which the fermions are bound states of smaller entities-primitive charges (preons). The preon is regarded as a dislocation in a dual 3-dimensional manifold-a topological object with no properties, save its unit mass and unit charge. It is shown that the dualism of this manifold gives rise to a hierarchy of complex structures resembling by their properties three families of the fundamental fermions. Although just a scheme for building a model of elementary particles, this description yields a quantitative explanation of many observable particle properties, including their masses.