scholarly journals Field theories with higher-group symmetry from composite currents

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Group Structure ◽  
Grassmann Algebra ◽  
Mathematical Structure ◽  
Point Particle ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Broken Symmetries ◽  
Ordinary Point ◽  
Categorical Groups

Abstract Higher-form symmetries are associated with transformations that only act on extended objects, not on point particles. Typically, higher-form symmetries live alongside ordinary, point-particle (0-form), symmetries and they can be jointly described in terms of a direct product symmetry group. However, when the actions of 0-form and higher-form symmetries become entangled, a more general mathematical structure is required, related to higher categorical groups. Systems with continuous higher-group symmetry were previously constructed in a top-down manner, descending from quantum field theories with a specific mixed ’t Hooft anomaly. I show that higher-group symmetry also naturally emerges from a bottom-up, low-energy perspective, when the physical system at hand contains at least two different given, spontaneously broken symmetries. This leads generically to a hierarchy of emergent higher-form symmetries, corresponding to the Grassmann algebra of topological currents of the theory, with an underlying higher-group structure. Examples of physical systems featuring such higher-group symmetry include superfluid mixtures and variants of axion electrodynamics.

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

scholarly journals 2-Group global symmetries and anomalies in six-dimensional quantum field theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clay Córdova ◽  
Thomas T. Dumitrescu ◽  
Kenneth Intriligator
Keyword(s):  
Global Symmetries ◽  
Group Symmetry ◽  
Field Theories ◽  
Global Symmetry ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Six Dimensions ◽  
String Theories

Abstract We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength f(2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J(2)∼ ∗Tr (f(2) ∧ f(2)). We show that suitable mixed anomalies involving the gauge field f(2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J(2). We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

scholarly journals On spontaneous wave function collapse and quantum field theory

2006 ◽  
Vol 462 (2070) ◽  
pp. 1897-1908 ◽  
Author(s):  
Roderich Tumulka
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Mathematical Structure ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Stochastic Evolution ◽  
Explicit Model ◽  
Natural Way ◽  
Grw Model

One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini & Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focusing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way.

Gauge Field Theory in Natural Geometric Language

2020 ◽  
Author(s):  
Daniel Canarutto
Keyword(s):  
Particle Physics ◽  
Quantum Physics ◽  
Brst Symmetry ◽  
Natural Extension ◽  
Integrated Approach ◽  
Arbitrary Spin ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Standard View ◽  
Spinor Bundle

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

scholarly journals Categorification of algebraic quantum field theories

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Universal Algebra ◽  
Finite Groups ◽  
Physical Interpretation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

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