A gauge theory of CPT transformations to first order

The CPT symmetry is made local for the Dirac field and an analogous local symmetry is proposed for curved spacetime. A nontrivial, infinitesimal variation of the Dirac action is thus induced. It is shown that the metric spin connection of general relativity cannot accommodate this symmetry. A new gauge field is therefore introduced, which turns out to be a real pseudovector field, and its equations of motion are derived.     

Finsler gauge transformations and general relativity

The theory of gauge transformations in Finsler space is applied to general relativity. It is seen that the transformations produce new metrics which correspond to the introduction of physical fields. The geodesic equation in the transformed space is equivalent to the equation of motion in the original space where the field is included by a force term. An example is given of a transformation and resulting metric in which the electromagnetic potential is related to parameters of the gauge transformation rather than to gauge potentials. This implies that the electromagnetic field corresponds to a connection instead of a curvature. Another example is given which shows how Weyl or conformal transformations are related to a class of the gauge transformations.     

Moving frame transport and gauge transformations

An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed.     

Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. Received: 17 July 2000 / Published online: 31 August 2000     

Solving the KP hierarchy by gauge transformations

We show that it is convenient to use gauge transformations (sometimes called explicit Bäcklund transformations) to generate new solutions for the KP hierarchy. Two particular kinds of gauge transformation operators, constructed out of the initial wave functions, are of fundamental importance in this approach. Through such gauge transformations, a very simple formula for the tau-function is obtained, encompassing and unifying all kinds of existing solutions. The corresponding free fermion representation and Baker functions for the new function can also be constructed.Communicated by S.-T. Yau     

Fields,observables and gauge transformations II

We wish to study the construction of charge-carrying fields given the representation of the observable algebra in the sector of states of zero charge. It is shown that the set of those covariant sectors which can be obtained from the vacuum sector by acting with localized automorphisms has the structure of a discrete Abelian group. An algebra of fields can be defined on the Hilbert space of a representation of the observable algebra which contains each of the above sectors exactly once. The dual group of acts as a gauge group on in such a way that is the gauge invariant part of is made up of Bose and Fermi fields and is determined uniquely by the commutation relations between spacelike separated fields.     

Spontaneous symmetry breaking and constant gauge transformations

Symmetry breaking solutions of several model theories are investigated with the result that constant gauge transformations of the fields describing zero mass Goldstone particles are responsible for the formal possibility of the spontaneous symmetry breaking.

     

The gauge transformations of the Schwinger model

We determine the group of implementable local gauge transformations of massless quantum electrodynamics in two space-time dimensions in the covariant Landau gauge. It splits into an infinite discrete set of disjoint classes. The unitary operators representing the implementable gauge transformations are constructed explicitly. A subset of these operators does not reduce to multiples of the identity in the physical Hilbert space constructed according to the usual rules. The disappearance of the fermionic degrees of freedom is related to this fact. Combined with the properties of the global chiral transformations, it provides a better understanding of the model's vacuum structure.     

Fields,observables and gauge transformations I

Starting from an algebra of fields and a compact gauge group of the first kind , the observable algebra is defined as the gauge invariant part of . A gauge group of the first kind is shown to be automatically compact if the scattering states are complete and the mass and spin multiplets have finite multiplicity. Under reasonable assumptions about the structure of it is shown that the inequivalent irreducible representations of (sectors) which occur are in one-to-one correspondence with the inequivalent irreducible representations of and that all of them are strongly locally equivalent. An irreducible representation of satisfies the duality property only if the sector corresponds to a 1-dimensional representation of . If is Abelian the sectors are connected to each other by localized automorphisms.On leave of absence from Instituto di Fisica G. Marconi, Università di Roma.     

Invariance of fermion determinant under large gauge transformations

We argue that in the perturbative framework the natural symmetry of the fermionic determinant is the perturbative gauge transformation (p.g.t.) which differs from the usual gauge transformation of the effective action through the absence of terms independent of the coupling constant. Calculated in a non-perturbative framework appropriate for large gauge function, the sum of these latter terms vanish. In three dimensions the invariance of the full fermion determinant under large gauge transformations is thus ensured due to the invariance under p.g.t. of the Chern-Simons term arising in some perturbative regularisations.     

Point transformations and renormalization in the unitary gauge

It is shown by means of a model that the renormalization and unitary gauges can be connected by a point transformation, and this fact is used to construct a formal proof of renormalization in the unitary gauge. The formal proof is then verified by demonstrating that for a fourth-order on-shell scattering process the S-matrix calculated directly in the unitary gauge is exactly equal to that calculated in the renormalization gauge. The calculation is refined to the point where it becomes purely graphical and this allows one to see by inspection how the cancellation of divergences occurs in the unitary gauge. The model considered here is Abelian, but it will be generalized to the non-Abelian case subsequently.     

Gauge transformations and quantum mechanics II. Physical interpretation of classical gauge transformations

New gauges are introduced. The potentials, vector and scalar, in these gauges are obtained in closed forms by the Green's function method. These closed form solutions are explicity expressed only in terms of the charge and current densities. The physical interpretation is on how potentials propagate from the charge and current densities. The Coulomb gauge and the Lorentz gauge are special cases of a new gauge defined in this paper. It is called the complete α-Lorentz gauge. The scalar potential propagates at speed αc from the charge density for any positive α. When α is one, the usual solutions for the Lorentz gauge are recovered. When α is not one, our results show that, in order to satisfy the requirement that electromagnetic fields be gauge invariant and in order to conform to Maxwell's interpretation that electromagnetic fields propagate at speed c from the charge and current densities (we only consider the vacuum), the vector potential must contain two mathematically and physically independent gradient components. Furthermore, one such component must propagate at speed αc while the other must at speed c from charge and current densities. Our discussions on the Coulomb gauge are based on the results obtained by letting α go to (positive) infinity. Guided by Maxwell's interpretation, we introduce a new decomposition of the vector potential in the Lorentz gauge into a longitudinal and a transverse component. For an arbitrary charge and current distribution, it is shown that the transverse component will generate all the fields only in the radiation zone. However, for a point charged particle, the transverse component only generates the “free fields”everywhere in the instantaneous rest frame of the charged particle.     

Field dependent nilpotent symmetry for gauge theories

We present predictions for the inclusive production of D mesons at the CERN LHC in the general-mass variable-flavor-number scheme at next-to-leading order. Detailed numerical results are compared to data where available, or presented in a way to ease future comparisons with experimental results. We also point out that measurements at large rapidity have the potential to pin down models of intrinsic charm.     

Differential calculus and gauge transformations on a deformed space

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory. Dedicated to the 60th birthday of Prof. Obregon.     

Solving the constrained modified KP hierarchy by gauge transformations

In this paper, we mainly investigate two kinds of gauge transformations for the constrained modified KP hierarchy in Kupershmidt-Kiso version. The corresponding gauge transformations are required to keep not only the Lax equation but also the Lax operator. For this, by selecting the special generating eigenfunction and adjoint eigenfunction, the elementary gauge transformation operators of modified KP hierarchy T_D(Φ) = (Φ^?1)^?_x¹? Φ^?1 and T_I (Ψ) = Ψ^?1? ^?1Ψ_x, become the ones in the constrained case. Finally, the corresponding successive applications of T_D and T_I on the eigenfunction Φ and the adjoint eigenfunction Ψ are discussed.     

Lorentz invariance,approach to helicity,and gauge transformations for Spin-1

Spin-1 fields are constructed automatically using the regular representation of the three-dimensional complex orthogonal group and the group's isomorphism with the Lorentz group. The fields and potentials are examined as one lets their mass go to zero. Going to masslessness after the differentiation of potentials results in a consistent formulation of the fields. The behavior of the massive and massless potentials under rotations in the particle frame is examined. The loss of global degrees of freedom as one goes from one to the other is made up by the appearance of gradient terms.