scholarly journals Holism as the empirical significance of symmetries

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Henrique Gomes
Keyword(s):  
Thought Experiment ◽  
Philosophy Of Physics ◽  
Newtonian Mechanics ◽  
Intrinsic State ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Good Grasp ◽  
Empirical Significance ◽  
The Universe

AbstractNot all symmetries are on a par. For instance, within Newtonian mechanics, we seem to have a good grasp on the empirical significance of boosts, by applying it to subsystems. This is exemplified by the thought experiment known as Galileo’s ship: the inertial state of motion of a ship is immaterial to how events unfold in the cabin, but is registered in the values of relational quantities such as the distance and velocity of the ship relative to the shore. But the significance of gauge symmetries seems less clear. For example, can gauge transformations in Yang-Mills theory—taken as mere descriptive redundancy—exhibit a similar relational empirical significance as the boosts of Galileo’s ship? This question has been debated in the last fifteen years in philosophy of physics. I will argue that the answer is ‘yes’, but only for a finite subset of gauge transformations, and under special conditions. Under those conditions, we can mathematically identify empirical significance with a failure of supervenience: the state of the Universe is not uniquely determined by the intrinsic state of its isolated subsystems. Empirical significance is therefore encoded in those relations between subsystems that stand apart from their intrinsic states.

CLASSICAL YANG-MILLS THEORY WITH FERMIONS I: GENERAL PROPERTIES OF A SYSTEM WITH CONSTRAINTS

1995 ◽  
Vol 10 (25) ◽  
pp. 3531-3579 ◽  
Author(s):  
LUCA LUSANNA
Keyword(s):  
Principal Bundle ◽  
Winding Number ◽  
Hamiltonian Description ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Minkowski Space Time ◽  
Small Gauge ◽  
Simply Connected ◽  
Gribov Ambiguity

A review is made of the basic properties of the Hamiltonian description of classical Yang-Mills theory with fermions described by Grassmann-valued Dirac spinors, in the case of a trivial principal bundle with a compact, semisimple, connected, simply connected Lie structure group over Minkowski space-time. The Poincaré group is assumed to be globally implementable and only the field configurations producing finite Poincaré generators are considered. A detailed study of the Hamiltonian group of gauge transformations is made, trying to elucidate the meaning of the global gauge transformations (connected with the non-Abelian charges and with the center of the gauge group), of the winding number (connected with the large gauge transformations and with the topological charge) and of the small gauge transformations generated by the first class constraints. This leads to the identification of boundary conditions on the gauge potentials and their conjugate momenta suitable for the Hamiltonian description and allowing covariance of the non-Abelian charges. Finally, a review is made of the problem of the Gribov ambiguity, whose basis is connected with the existence of stability subgroups of gauge transformations for certain gauge potentials (gauge symmetries) and/or certain field strengths (gauge copies) in generic Sobolev spaces.

scholarly journals NON-ABELIAN GAUGE SYMMETRIES INDUCED BY THE UNOBSERVABILITY OF EXTRA DIMENSIONS IN A KALUZA–KLEIN APPROACH

2006 ◽  
Vol 21 (03) ◽  
pp. 265-274 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Extra Dimensions ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Field Equations ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
The Right ◽  
Kaluza Klein

In this work we deal with the extension of the Kaluza–Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce field equations and gauge transformations in the four-dimensional picture. More precisely, in field equations any dependence on extra coordinates is canceled out by an integration, as consequence of the unobservability of extra dimensions. Thus, by virtue of this extra dimension unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein–Yang–Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang–Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.

Admissible boundary conditions for Hamiltonian field theories

2017 ◽  
Vol 14 (08) ◽  
pp. 1740006 ◽  
Author(s):  
Manuel Asorey ◽  
Alberto Ibort ◽  
Amelia Spivak
Keyword(s):  
Boundary Conditions ◽  
Level Set ◽  
Lagrangian Submanifolds ◽  
Moment Map ◽  
Field Theories ◽  
Manifolds With Boundary ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
The Moment

In the setting of a multisymplectic formalism for Hamiltonian theories on manifolds with boundary a class of admissible boundary conditions based on the principle of preservation of the gauge symmetries of the theory is presented. Such admissible conditions are characterized as those boundary conditions determined by Lagrangian submanifolds on the space of fields at the boundary lying in the zero level set of the moment map of the group of gauge transformations at the boundary. The examples of gauge covariant fields and pure Yang–Mills theories are analyzed.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Gauging the higher-spin-like symmetries by the Moyal product

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
M. Cvitan ◽  
P. Dominis Prester ◽  
S. Giaccari ◽  
M. Paulišić ◽  
I. Vuković
Keyword(s):  
Linear Connection ◽  
Covariant Formulation ◽  
Formal Similarity ◽  
Commutative Field ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Derivative ◽  
Novel Approach ◽  
Emergent Geometry ◽  
Higher Spin

Abstract We analyze a novel approach to gauging rigid higher derivative (higher spin) symmetries of free relativistic actions defined on flat spacetime, building on the formalism originally developed by Bonora et al. and Bekaert et al. in their studies of linear coupling of matter fields to an infinite tower of higher spin fields. The off-shell definition is based on fields defined on a 2d-dimensional master space equipped with a symplectic structure, where the infinite dimensional Lie algebra of gauge transformations is given by the Moyal commutator. Using this algebra we construct well-defined weakly non-local actions, both in the gauge and the matter sector, by mimicking the Yang-Mills procedure. The theory allows for a description in terms of an infinite tower of higher spin spacetime fields only on-shell. Interestingly, Euclidean theory allows for such a description also off-shell. Owing to its formal similarity to non-commutative field theories, the formalism allows for the introduction of a covariant potential which plays the role of the generalised vielbein. This covariant formulation uncovers the existence of other phases and shows that the theory can be written in a matrix model form. The symmetries of the theory are analyzed and conserved currents are explicitly constructed. By studying the spin-2 sector we show that the emergent geometry is closely related to teleparallel geometry, in the sense that the induced linear connection is opposite to Weitzenböck’s.

scholarly journals Trace dynamics and division algebras: towards quantum gravity and unification

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Lie Group ◽  
Planck Scale ◽  
The Self ◽  
Division Algebras ◽  
Quantum Field ◽  
Octonion Algebra ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Massless Spin ◽  
Correct Understanding

AbstractWe have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann matrices. Evolution takes place in Connes time. At energies much lower than Planck scale, trace dynamics reduces to quantum field theory. In the present paper, we explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. The automorphisms of the octonion algebra, which belong to the smallest exceptional Lie group G2, replace space-time diffeomorphisms and internal gauge transformations, bringing them under a common unified fold. Building on earlier work by other researchers on division algebras, we propose the Lorentz-weak unification at the Planck scale, the symmetry group being the stabiliser group of the quaternions inside the octonions. This is one of the two maximal sub-groups of G2, the other one being SU(3), the element preserver group of octonions. This latter group, coupled with U(1)em, describes the electrocolour symmetry, as shown earlier by Furey. We predict a new massless spin one boson (the ‘Lorentz’ boson) which should be looked for in experiments. Our Lagrangian correctly describes three fermion generations, through three copies of the group G2, embedded in the exceptional Lie group F4. This is the unification group for the four fundamental interactions, and it also happens to be the automorphism group of the exceptional Jordan algebra. Gravitation is shown to be an emergent classical phenomenon. Although at the Planck scale, there is present a quantised version of the Lorentz symmetry, mediated by the Lorentz boson, we argue that at sub-Planck scales, the self-adjoint part of the octonionic trace dynamics bears a relationship with string theory in 11 dimensions.

scholarly journals Higgsing towards E-strings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Kimyeong Lee
Keyword(s):  
String Theory ◽  
Gauge Theories ◽  
The Self ◽  
Flavor Symmetry ◽  
Strongly Coupled ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
Elliptic Genera ◽  
Linear Sigma Models

Abstract We explore 6d (1, 0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an E8 wall. Specifically, we study the 2d $$ \mathcal{N} $$ N = (0, 4) gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0, 4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the E8 wall, and find their fully refined elliptic genera.

scholarly journals CANONICAL APPROACH TO 2D SUPERSYMMETRIC WZNW MODEL COUPLED TO SUPERGRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 1923-1936 ◽  
Author(s):  
OLIVERA MIŠKOVIĆ ◽  
BRANISLAV SAZDOVIĆ
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Moody Algebra ◽  
Gauge Transformations ◽  
Local Gauge ◽  
Gauge Symmetries ◽  
Wznw Model ◽  
Canonical Approach ◽  
Explicit Expressions

Starting from the known representation of the Kac–Moody algebra in terms of the coordinates and momenta, we extend it to the representation of the super Kac–Moody and super Virasoro algebras. Then we use general canonical method to construct an action invariant under local gauge symmetries, where components of the super energy–momentum tensor L± and G± play the role of the diffeomorphisms and supersymmetry generators respectively. We obtain covariant extension of WZNW theory with respect to local supersymmetry as well as explicit expressions for gauge transformations.

Time’s Arrow and Statistical Uncertainty in Physics and Philosophy

2020 ◽  
pp. 204-241
Author(s):  
Theodore M. Porter
Keyword(s):  
Free Will ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Statistical Uncertainty ◽  
Newtonian Mechanics ◽  
Historical School ◽  
James Clerk Maxwell ◽  
Objective Chance ◽  
The Universe ◽  
Time’S Arrow

This chapter explores how German economists and statisticians of the historical school viewed the idea of social or statistical law as the product of confusion between spirit and matter or, equivalently, between history and nature. That the laws of Newtonian mechanics are fully time-symmetric and hence can be equally run backwards or forwards could not easily be reconciled with the commonplace observation that heat always flows from warmer to cooler bodies. James Clerk Maxwell, responding to the apparent threat to the doctrine of free will posed by thermodynamics and statistics, pointed out that the second law of thermodynamics was only probable, and that heat could be made to flow from a cold body to a warm one by a being sufficiently quick and perceptive. Ludwig Boltzmann resisted this incursion of probabilism into physics but in the end he was obliged, largely as a result of difficulties presented by the issue of mechanical reversibility, to admit at least the theoretical possibility of chance effects in thermodynamics. Meanwhile, the American philosopher and physicist C. S. Pierce determined that progress—the production of heterogeneity and homogeneity—could never flow from rigid mechanical laws, but demanded the existence of objective chance throughout the universe.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

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