Construction of a translation-invariant U(N) damped noncommutative gauge model

2020 ◽  
Vol 35 (22) ◽  
pp. 2050118
Author(s):  
Ouahiba Toumi ◽  
Smain Kouadik
Keyword(s):  
Covariant Derivative ◽  
Torsion Tensor ◽  
Tree Level ◽  
Dirac Field ◽  
Translation Invariance ◽  
Group Model ◽  
Translation Invariant ◽  
Yang Mills ◽  
Interaction Term ◽  
Popov Ghost

We have built a noncommutative unitary gauge group model preserving translation invariance. It describes the interaction of the Dirac field with the gauge field. The interaction term is expanded as a power series resulting from the introduction of the inverse covariant derivative. The consistency of the model is sustained by the fact that the Ward identity holds at tree level. The pure Yang–Mills action, including the fixing term and the Faddeev–Popov ghost term were constructed. It is striking that the commutator of our covariant derivative contained the torsion tensor, in addition to the field strength from which the Yang–Mills action was built.

scholarly journals Evaluating EYM amplitudes in four dimensions by refined graphic expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hongxiang Tian ◽  
Enze Gong ◽  
Chongsi Xie ◽  
Yi-Jian Du
Keyword(s):  
Tree Level ◽  
Tree Amplitude ◽  
Four Dimensions ◽  
Yang Mills ◽  
Negative Helicity ◽  
Spanning Forests ◽  
Single Trace

Abstract The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − or $$ \left({h}_i^{-},{g}_j^{-}\right) $$ h i − g j − configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

scholarly journals On B- Covariant Derivative of First Order for Some Tensors in different Spaces

2021 ◽  
Vol 2 (2) ◽  
pp. 30-37
Author(s):  
Alaa A. Abdallah ◽  
A. A. Navlekar ◽  
Kirtiwant P. Ghadle
Keyword(s):  
Curvature Tensor ◽  
Covariant Derivative ◽  
Torsion Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Recurrence Property ◽  
Necessary And Sufficient ◽  
The Relationship

In this paper, we study the relationship between Cartan's second curvature tensor $P_{jkh}^{i}$ and $(h) hv-$torsion tensor $C_{jk}^{i}$ in sense of Berwald. Moreover, we discuss the necessary and sufficient condition for some tensors which satisfy a recurrence property in $BC$-$RF_{n}$, $P2$-Like-$BC$-$RF_{n}$, $P^{\ast }$-$BC$-$RF_{n}$ and $P$-reducible-$BC-RF_{n}$.

Extension of Monotonic Functions and Representation of Preferences

2021 ◽  
Author(s):  
Özgür Evren ◽  
Farhad Hüsseinov
Keyword(s):  
Dominance Relation ◽  
Translation Invariance ◽  
Compact Set ◽  
Continuous Real Function ◽  
Translation Invariant ◽  
Extension Theorems ◽  
Topological Vector Spaces ◽  
Dominance Relations ◽  
Universal Space ◽  
Vector Structure

Consider a dominance relation (a preorder) ≿ on a topological space X, such as the greater than or equal to relation on a function space or a stochastic dominance relation on a space of probability measures. Given a compact set K ⊆ X, we study when a continuous real function on K that is strictly monotonic with respect to ≿ can be extended to X without violating the continuity and monotonicity conditions. We show that such extensions exist for translation invariant dominance relations on a large class of topological vector spaces. Translation invariance or a vector structure are no longer needed when X is locally compact and second countable. In decision theoretic exercises, our extension theorems help construct monotonic utility functions on the universal space X starting from compact subsets. To illustrate, we prove several representation theorems for revealed or exogenously given preferences that are monotonic with respect to a dominance relation.

scholarly journals Generalization of the Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630003 ◽  
Author(s):  
G. Savvidy
Keyword(s):  
Beta Function ◽  
Coupling Constants ◽  
Standard Theory ◽  
Large Integer ◽  
Tree Level ◽  
Gauge Fields ◽  
Gauge Bosons ◽  
Yang Mills ◽  
Conformally Invariant ◽  
Vector Gauge

We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang–Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The proposed extension is essentially based on the extension of the Poincaré algebra and the existence of an appropriate transversal representations. The invariant Lagrangian is expressed in terms of new higher-rank field strength tensors. It does not contain higher derivatives of tensor gauge fields and all interactions take place through three- and four-particle exchanges with a dimensionless coupling constant. We calculated the scattering amplitudes of non-Abelian tensor gauge bosons at tree level, as well as their one-loop contribution into the Callan–Symanzik beta function. This contribution is negative and corresponds to the asymptotically free theory. Considering the contribution of tensorgluons of all spins into the beta function we found that it is leading to the theory which is conformally invariant at very high energies. The proposed extension may lead to a natural inclusion of the standard theory of fundamental forces into a larger theory in which vector gauge bosons, leptons and quarks represent a low-spin subgroup. We consider a possibility that inside the proton and, more generally, inside hadrons there are additional partons — tensorgluons, which can carry a part of the proton momentum. The extension of QCD influences the unification scale at which the coupling constants of the Standard Model merge, shifting its value to lower energies.

scholarly journals SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Dirac Field ◽  
Spin Connection ◽  
Yang Mills ◽  
Object A ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
The Right ◽  
Kaluza Klein

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

scholarly journals Kinetics of Recovery of the Dark-adapted Salamander Rod Photoresponse

1998 ◽  
Vol 111 (1) ◽  
pp. 7-37 ◽  
Author(s):  
S. Nikonov ◽  
N. Engheta ◽  
E.N. Pugh
Keyword(s):  
Theoretical Analysis ◽  
Time Constant ◽  
Translation Invariance ◽  
Flash Intensity ◽  
Translation Invariant ◽  
Calcium Dependent ◽  
The Difference ◽  
Analytical Expressions ◽  
Kinetics Of ◽  
Flash Response

The kinetics of the dark-adapted salamander rod photocurrent response to flashes producing from 10 to 105 photoisomerizations (Φ) were investigated in normal Ringer's solution, and in a choline solution that clamps calcium near its resting level. For saturating intensities ranging from ∼102 to 104 Φ, the recovery phases of the responses in choline were nearly invariant in form. Responses in Ringer's were similarly invariant for saturating intensities from ∼103 to 104 Φ. In both solutions, recoveries to flashes in these intensity ranges translated on the time axis a constant amount (τc) per e-fold increment in flash intensity, and exhibited exponentially decaying “tail phases” with time constant τc. The difference in recovery half-times for responses in choline and Ringer's to the same saturating flash was 5–7 s. Above ∼104 Φ, recoveries in both solutions were systematically slower, and translation invariance broke down. Theoretical analysis of the translation-invariant responses established that τc must represent the time constant of inactivation of the disc-associated cascade intermediate (R*, G*, or PDE*) having the longest lifetime, and that the cGMP hydrolysis and cGMP-channel activation reactions are such as to conserve this time constant. Theoretical analysis also demonstrated that the 5–7-s shift in recovery half-times between responses in Ringer's and in choline is largely (4–6 s) accounted for by the calcium-dependent activation of guanylyl cyclase, with the residual (1–2 s) likely caused by an effect of calcium on an intermediate with a nondominant time constant. Analytical expressions for the dim-flash response in calcium clamp and Ringer's are derived, and it is shown that the difference in the responses under the two conditions can be accounted for quantitatively by cyclase activation. Application of these expressions yields an estimate of the calcium buffering capacity of the rod at rest of ∼20, much lower than previous estimates.

Linear Programming Performance Bounds for Markov Chains With Polyhedrally Translation Invariant Probabilities and Applications to Unreliable Manufacturing Systems and Enhanced Wafer Fab Models

2002 ◽  
Author(s):  
James R. Morrison ◽  
P. R. Kumar
Keyword(s):  
Markov Chains ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Transition Probabilities ◽  
Invariance Property ◽  
Translation Invariance ◽  
Performance Bounds ◽  
Translation Invariant ◽  
Wafer Fab ◽  
Index Policies

Our focus is on a class of Markov chains which have a polyhedral translation invariance property for the transition probabilities. This class can be used to model several applications of interest which feature complexities not found in usual models of queueing networks, for example failure prone manufacturing systems which are operating under hedging point policies, or enhanced wafer fab models featuring batch tools and setups or affine index policies. We present a new family of performance bounds which is more powerful both in expressive capability as well as the quality of the bounds than some earlier approaches.

scholarly journals R Symmetry and the Topological Twist of N = 2 Effective Supergravities of Heterotic Strings

1997 ◽  
Vol 12 (02) ◽  
pp. 379-418 ◽  
Author(s):  
Marco Billó ◽  
Pietro Fré ◽  
Riccardo D'auria ◽  
Sergio Ferrara ◽  
Paolo Soriani ◽  
...  
Keyword(s):  
Gauge Theories ◽  
The Other ◽  
Tree Level ◽  
Vector Multiplet ◽  
Continuous Symmetry ◽  
Yang Mills ◽  
Heterotic Strings ◽  
Axion Field ◽  
Effective Theories ◽  
R Symmetry

We discuss R symmetries in locally supersymmetric N = 2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton–axion field has different R charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang–Mills instantons with triholomorphic hyperinstantons and axion instantons. For the tree level classical special manifolds ST(n) = SU(1,1)/U(1) × SO(2,n)/[SO(2) × SO(n)], R symmetry with the specified properties is a continuous symmetry, but for the quantum-corrected manifolds [Formula: see text] a discrete R group of electric–magnetic duality rotations is sufficient and we argue that it exists.

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