Non Gauge Theories Research Articles

Infrared dressing in real time: Emergence of anomalous dimensions

We implement a dynamical resummation method (DRM) as an extension of the dynamical renormalization group to study the time evolution of infrared dressing in non-gauge theories. Super renormalizable and renormalizable models feature infrared divergences similar to those of a theory at a critical point, motivating a renormalization group improvement of the propagator that yields a power law decay of the survival probability $\propto t^{-\Delta}$. The (DRM) confirms this decay, yields the dressed state and determines that the anomalous dimension $\Delta$ is completely determined by the slope of the spectral density at threshold independent of the ultraviolet behavior, suggesting certain universality for infrared phenomena. The dressed state is an entangled state of the charged and massless quanta. The entanglement entropy is obtained by tracing over the unobserved massless quanta. Its time evolution is determined by the (DRM), it is infrared finite and describes the information flow from the initial single particle to the asymptotic multiparticle dressed state. We show that effective field theories of massless axion-like particles coupled to fermion fields do not feature infrared divergences, and provide a criterion for infrared divergences in effective field theories valid for non-gauge theories up to one loop.

Notes on lattice observables for parton distributions: nongauge theories

We review recent theoretical developments concerning the definition and the renormalization of equal-time correlators that can be computed on the lattice and related to Parton Distribution Functions (PDFs) through a factorization formula. We show how these objects can be studied and analyzed within the framework of a nongauge theory, gaining insight through a one-loop computation. We use scalar field theory as a playground to revise, analyze and present the main features of these ideas, to explore their potential, and to understand their limitations for extracting PDFs. We then propose a framework that would allow to include the available lattice QCD data in a global analysis to extract PDFs.

The generalised infrared structure of the gluon propagator

Gauge theory correlators are potentially more singular in the infrared than those in non-gauge theories. We determine the implications that these singularities have on the spectrum of the theory, proving that the appearance of generalised poles implies the existence of on-shell states with fixed mass, but zero norm. For quantum chromodynamics these poles have direct relevance for the confinement of coloured states. Using lattice data for the Landau gauge gluon propagator we subsequently test for the presence of these poles, establishing that the data is indeed consistent with such a component.

Mathematical Feature of Gauge Theory

In this paper, we deal with root of gauge theory and constrained system. Considering unlike second class constrained leads to non-gauge theory, all theories with first class constraints are gauge theory. We consider two mathematical and systematic methods, BFT approach and Gauge Unfixing formalism which do conversion of non-gauge theory into gauge one. Despite of noble similarities of two methods, they have primordial different which mentioned. In the end, we figure out these methods for two impressive models which are interesting in their own

Factorization of theS3/Znpartition function

We investigate ${\mathbit{S}}^{3}/{\mathbb{Z}}_{n}$ partition function of three-dimensional $\mathcal{N}=2$ supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative signs among the contributions. We argue that the factorization to holomorphic blocks is a useful criterion to determine the signs and propose a formula for them. We show that the orbifold partition function of a general nongauge theory is correctly factorized provided that we take appropriate relative signs. We also present a few examples of gauge theories. We point out that the sign factor for the orbifold partition function is closely related to a similar sign factor in the lens space index and the three-dimensional index.

Experimental Investigation of the Traction Force for a New Space Thruster

A long course of experimental investigations of a new non-gauge force used for the traction of a prototype space thruster placed on board an hemispherical ship are reviewed and discussed. The physical nature of the new force is explained by the theory of byuon, a non-gauge theory of the formation of the physical space and the world of ultimate particles from some unobservable objects called “byuons”. The definition of these objects contains a new fundamental vector constant, the cosmological vector potential Ag, which direction defines a marginal global anisotropy of the physical space. The experimental results show a remarkable dependence of the force on the period of the year and even on the time of the day, the details of such dependence suggesting astronomical coordinates of the vector Ag which are consistent with previous estimates yet reducing their uncertainty: in the second equatorial coordinates system, the right ascension α=316°±5° and the declination δ=36°±10° are obtained. The level of the traction force during the experimental period turns out to be in the range 2.5 mN to 51 mN, while the best figure for the power to thrust ratio as derived from previous experiments is 330 W/N, suggestive of its potential competitiveness with state of the art electric propulsion thrusters.

Covariant basis induced by parity for the(j,0)⊕(0,j)representation

In this work, we build a covariant basis for operators acting on the $(j,0)\oplus(0,j)$ Lorentz group representations. The construction is based on an analysis of the covariant properties of the parity operator, which for these representations transforms as the completely temporal component of a symmetrical tensor of rank $2j$. The covariant properties of parity involve the Jordan algebra of anti commutators of the Lorentz group generators which unlike the Lie algebra is not universal. We make the construction explicit for $j=1/2,1$ and $3/2$, reproducing well-known results for the $j=1/2$ case. We provide an algorithm for the corresponding calculations for arbitrary $j$. This covariant basis provides an inventory of all the possible interaction terms for gauge and non-gauge theories of fields for these representations. In particular, it supplies a single second rank antisymmetric structure, which in the Poincar\'e projector formalism implies a single Pauli term arising from gauge interactions and a single (free) parameter $g$, the gyromagnetic factor. This simple structure predicts that for an elementary particle in this formalism all multipole moments, $Q^{l}_{E}$ and $Q^{l}_{M}$, are dictated by the complete algebraic structure of the Lorentz generators and the value of $g$. We explicitly calculate the multipole moments, for arbitrary $j$ up to $l=8$. Comparing with results in the literature we find that only the electric charge and magnetic moment of a spin $j$ particle are independent of the Lorentz representation under which it transforms, all higher multipoles being representation dependent. Finally we show that the propagation of the corresponding spin $j$ waves in a electromagnetic background is causal.

S 3/Z n partition function and dualities

We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle points with different holonomies. An appropriate choice of the phase of each contribution is essential to obtain the partition function. We determine the relative phases in the holonomy sum in a few examples by using duality to non-gauge theories. In the case of odd n the phase factors can be absorbed by modifying a single function appearing in the partition function.

An extension of Pohlmeyer's theorem

Applying the exact renormalization group to scalar field theory in Euclidean space of general (not necessarily integer) dimension, it is proven that the only fixed point with vanishing anomalous dimension is the Gaussian one. The proof requires positivity of the two-point connected correlation function together with a technical assumption concerning solutions of the flow equation. The method, in which the representation of the flow equation as a heat equation plays a central role, extends directly to non-gauge theories with arbitrary matter content (though nonlinear sigma models are beyond the scope of the current method).

Monte Carlo event generators at nonleading order

A method to construct Monte Carlo event generators at arbitrarily nonleading order is explained for the case of a nongauge theory. A precise and correct treatment of parton kinematics is provided. Modifications of the conventional formalism are required: parton showering is not exactly the same as Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution, and the external line prescription for the hard scattering differs from the Lehmann-Symanzik-Zimmermann prescription. The prospects for extending the results to QCD are discussed.

QUANTUM AND CLASSICAL GAUGE SYMMETRIES IN A MODIFIED QUANTIZATION SCHEME

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the nonlinear gauge [Formula: see text] of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional local Faddeev–Popov formula without taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive nongauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge-invariant, has a more intrinsic meaning. It is suggested that we extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.

Non-supersymmetric vacua and the D-flatness condition

Some N = 1 gauge theories, including SQED and N F = 1 SQCD, have the property that, for arbitrary superpotentials, all stationary points of the potential V = F + D are D-flat. For others, stationary points of V are complex gauge transformations of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.

Geometric interpretation for the Wess-Zumino terms

We propose a geometric interpretation for the Wess-Zumino (WZ) constraint converting method. This study is done in the context of nonlinearly constrained systems, formulated as gauge theories. A deep unifying concept is revealed connecting the invariant and the noninvariant models disclosing a unique relationship between the WZ gauge orbits with the nonlinear surfaces. Such structures unveil the physical and geometrical meaning of the WZ terms in turning second-class constraints into gauge generators quantities. A simple and practical mapping between gauge and nongauge theories is found, providing a new interpretation for the nonlinear constraint as the natural gauge fixing surface for the gauge theories.

Possibility of constructing a gauge-invariant quantum formulation for nongauge classical theory

A general method is proposed for the construction of a gauge-invariant canonical quantum formulation for the gauge-invariant classical theory that depends on the set of parameters. The conditions for closure of the algebra of operators, which generate quantum gauge transformations, entails constraints on the parameters of the theory. The approach described is demonstrated by the example of a closed bosonic string, interacting with a background tachyonic field. The condition of a mass shell for the tachyon is reproduced within the framework of the proposed canonical formulation.

ON A GAUGE INVARIANT QUANTUM FORMULATION FOR NON-GAUGE CLASSICAL THEORY

We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon is produced.

Sogami's Generalized Covariant Derivative and Non-Commutative Differential Geometry

It is shown that there exists a close connection between Sogami's method in the standard model and our previous formulation of non-commutative differential geometry. This connection emerges from an identification of an extra one-form basis in the latter with an ordinary one-form valued in Dirac algebra. Application of the method to the standard model with (or without) singlet va's gives a new intepretation of SU(5) relations among gauge coupling constants in the model without SU(5) symmetry. In a recent paper, 1 > Sogami proposed a new method of deriving the bosonic sector of the standard model lagrangian from the fermionic one in an ingenious way. This is based on the observation that the generalized covariant derivative, which acts on a set of chiral fermion fields (total fermion field) interacting with both gauge and Higgs fields, determines generalized field strengths by taking a commutator, which then fixes the bosonic lagrangian. This procedure is applied 2 > to both gauge and non-gauge theories by performing the usual chiral decomposition of the Dirac spinor so as to make the generalized covariant derivative a 2 X 2 matrix in chiral space. This matrix structure resembles that of non-commutative geometry (NCG) 3 > as for­

Sogami's Generalized Covariant Derivative in Gauge and Non-Gauge Theories

We describe Sogami's method of generating the bosonic sector of the standard model lagrangian from the generalized covariant derivative acting on chiral fermion fields in a simpler setting using well-known field theory models with either global or local symmetries. It is shown that Sogami's method is applicable not only to gauge theories but also to non-gauge theories. It is also shown that the present method offers a different interpretation of Sogami's high energy limit with SU(5) relations among gauge coupling constants in the standard model. Recently, SogamP) proposed an interesting method of generating the bosonic sector of the standard model lagrangian from the generalized covariant derivative operator acting on a set of chiral fermion fields (total fermion field). Its spirit is similar to Cannes' approach based on the non-commutative geometry, 2 ), 3 ), 4 ) but its mathematical nature is quite different, and much easier to understand, using more familiar tools. The purpose of this note is to show that Sogami's method is appli­ cable to both gauge and non-gauge theories in greater generality. We first explain it in terms of simpler field theory models with either global or local symmetries, and then re-study Sogami's reformulation of the standard model in a different setting described in this note. A gauge theory coupled to massive fermions of mass m is described by the lagrangian

Sogami's Generalized Covariant Derivative in Gauge and Non-Gauge Theories

Sogami's Generalized Covariant Derivative in Gauge and Non-Gauge Theories

Anomalies and renormalisation in the BRST-BV framework

The way in which irreducible gauge theories with open algebras give rise to Ward identities for the BRST symmetries is discussed. The possible obstructions to the implementation of these Ward identities are shown to obey consistency conditions. Similar techniques are also applicable in non-gauge theories with non-linear symmetries. The Wess-Zumino model is analysed as an example.

The parametrization and gauge invariant effective action of composite fields

Abstract The parametrization invariant off-shell effective action (EA) of composite fields is constructed in non-gauge theories. The generalization of this EA for gauge theories leads to the gauge invariant and gauge fixing independent EA of composite fields. The rule for the calculation of the one-loop unique EA of composite fields of g42 kind is obtained.