arXiv subjects

Marko Vojinovic

Publications and source records attributed to Marko Vojinovic.

At least 19 recordsLinked to original sources

arXiv2026

A 3BF model of quantum gravity coupled to Standard Model matter

We develop an explicit model of quantum gravity coupled to the matter fields of the Standard Model, based on the 3-group structure and the 3BF action, within the framework of higher gauge theory. The model is constructed by providing a rigorous definition for the path integral of the theory, achieved by defining the whole theory on a piecewise-flat spacetime manifold. To that end, we develop a method to systematically discretize both the action and the path integral measure by passing from a smooth manifold to a piecewise-flat manifold. Finally, we discuss in some detail the structure of the resulting quantum gravity model, and provide a preliminary analysis of its semiclassical limit.

hep-th↗

arXiv2025

Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity

We construct a correspondence between the quantized constrained 3BF theory and the quantized Einstein-Cartan theory with contact spin-spin interaction, both of which describe the Standard Model coupled to Einstein-Cartan gravitational field. First we introduce the expectation values of observables using the path integral formalism for both theories, and then by integrating out some configuration space variables in the quantum 3BF theory we obtain the definition of the corresponding observable in the quantum Einstein-Cartan theory with contact interaction. The correspondence is a rather general result, since it can be established without actually performing the detailed quantization of either theory. Finally, we discuss the differences in the predictions of the two theories on the example of the 4-volume density of spacetime, and on the example of gravitational waves.

gr-qc↗

arXiv2024

The 3BF theory as a TQFT

We study the path integral quantization of the topological 3BF theory, whose gauge symmetry is described by a 3-group. This theory is relevant for the quantization of general relativity coupled to Standard Model of elementary particles. We explicitly construct a state sum corresponding to the discretized path integral of a 3BF action. Being a topological invariant of 4-dimensional manifolds with boundary, this state sum gives rise to a topological quantum field theory (TQFT), realized as a functor between the category of cobordisms and the category of Hilbert spaces. After an introduction to appropriate category theory concepts and the construction of the state sum, we provide an explicit proof that it satisfies all Atiyah's axioms, and thus represents a genuine TQFT. The formulation of this TQFT represents a major step in the spinfoam quantization programme for a realistic theory of quantum gravity with matter.

hep-th↗

arXiv2024

Hamiltonian analysis of the BFCG theory for a strict Lie 2-group

We perform a complete Hamiltonian analysis of the BFCG action for a general Lie 2-group by using the Dirac procedure. We show that the resulting dynamical constraints eliminate all local degrees of freedom which implies that the BFCG theory is a topological field theory.

math-ph↗

arXiv2024

Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity

We study the details of the explicit and spontaneous symmetry breaking of the constrained 3BF action representing the Standard Model coupled to Einstein-Cartan gravity. First we discuss how each particular constraint breaks the original symmetry of the topological 3BF action. Then we investigate the spontaneous symmetry breaking and the Higgs mechanism for the electroweak theory in the constrained 3BF form, in order to demonstrate that they can indeed be performed in the framework of higher gauge theory. A formulation of the Proca action as a constrained 3BF theory is also studied in detail.

hep-th↗

arXiv2023

Challenges for extensions of the process matrix formalism to quantum field theory

We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when one attempts to move from particle ontology into the realm of field ontology, i.e., when one transitions from mechanics to field theory framework. These issues need to be addressed, and problems solved, if one aims to expand the scope of applicability of the process matrix formalism, and therefore its usefulness. This is far from a trivial and straightforward endeavour, but rather a task for a whole future research programme.

quant-ph↗

arXiv2023

Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories

When discussing the gauge symmetries of any theory, the Henneaux-Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux-Teitelboim transformations and the resulting gauge group in the general case, and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

hep-th↗

arXiv2023

Operational interpretation of the vacuum and process matrices for identical particles

This work overviews the single-particle two-way communication protocol recently introduced by del Santo and Dakić (dSD), and analyses it using the process matrix formalism. We give a detailed account of the importance and the operational meaning of the interaction of an agent with the vacuum -- in particular its role in the process matrix description. Our analysis shows that the interaction with the vacuum should be treated as an operation, on equal footing with all other interactions. This raises the issue of counting such operations in an operational manner. Motivated by this analysis, we apply the process matrix formalism to capped Fock spaces using the framework of second quantisation, in order to characterise protocols with an indefinite number of identical particles.

quant-ph↗

arXiv2022

Equivalence Principle in Classical and Quantum Gravity

We give a general overview of various flavors of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We also discuss its generalisation to a theory of quantum gravity. Our analysis suggests that only the strong equivalence principle can be considered fundamental enough to be generalised to a quantum gravity context, since all other flavors of equivalence principle hold only approximately already at the classical level.

gr-qc↗

arXiv2022

Operational verification of the existence of a spacetime manifold

We argue that there exists an operational way to establish the observability of the notions of space and time. Specifically, we propose a theory-independent protocol for a gedanken-experiment, whose outcome is a signal establishing the observability of the spacetime manifold, without a priori assuming its existence. The experimental signal contains the information about the dimension and the topology of spacetime (with the currently achievable precision), and establishes its manifold structure, while respecting its underlying diffeomorphism symmetry. We also introduce and discuss appropriate criteria for the concept of emergence of spacetime, which any tentative theoretical model of physics must satisfy in order to claim that spacetime does emerge from some more fundamental concepts.

gr-qc↗

arXiv2022

Gauge symmetry of the 3BF theory for a generic Lie 3-group

The higher category theory can be employed to generalize the BF action to the so-called 3BF action, by passing from the notion of a gauge group to the notion of a gauge 3-group. In this work we determine the full gauge symmetry of the 3BF action. To that end, the complete Hamiltonian analysis of the 3BF action for an arbitrary semistrict Lie 3-group is performed, by using the Dirac procedure. This analysis is the first step towards a canonical quantization of a 3BF theory. This is an important stepping-stone for the quantization of the complete Standard Model of elementary particles coupled to Einstein-Cartan gravity, formulated as a 3BF action with suitable simplicity constraints. We show that the resulting gauge symmetry group consists of the already familiar G-, H-, and L-gauge transformations, as well as additional M- and N-gauge transformations, which have not been discussed in the existing literature.

hep-th↗

arXiv2022

Topological invariant of 4-manifolds based on a 3-group

We study a generalization of a 4-dimensional BF-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum Z, based on the classical 3BF action for a general 3-group and a 4-dimensional spacetime manifold. This state sum coincides with Porter's TQFT for d=4 and n=3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum Z remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2BF action with the underlying 2-group structure.

hep-th↗

arXiv2021

Standard Model and 4-groups

We show that a categorical generalization of the the Poincaré symmetry which is based on the n-crossed modules becomes natural and simple when n=3 and that the corresponding 3-form and 4-form gauge fields have to be a Dirac spinor and a Lorentz scalar, respectively. Hence by using a Poincaré 4-group we naturally incorporate fermionic and scalar matter into the corresponding 4-connection. The internal symmetries can be included into the 4-group structure by using a 3-crossed module based on the $SL(2,\mathbb{C}) \times K$ group, so that for $K=U(1)\times SU(2) \times SU(3)$ we can include the Standard Model into this categorification scheme.

hep-th↗

arXiv2021

Quantum gravity and elementary particles from higher gauge theory

We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families.

hep-th↗

arXiv2020

Causal orders, quantum circuits and spacetime: distinguishing between definite and superposed causal orders

We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.

quant-ph↗

arXiv2020

Construction and examples of higher gauge theories

We provide several examples of higher gauge theories, constructed as generalizations of a BF model to 2BF and 3BF models with constraints. Using the framework of higher category theory, we introduce appropriate 2-groups and 3-groups, and construct the actions for the corresponding constrained 2BF and 3BF theories. In this way, we can construct actions which describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. Each action is naturally split into a topological sector and a sector with simplicity constraints. The properties of the higher gauge group structure opens up a possibility of a nontrivial unification of all fields.

gr-qc↗

arXiv2020

Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

The higher category theory can be employed to generalize the BF action to the so-called 3BF action, by passing from the notion of a gauge group to the notion of a gauge 3-group. The theory of scalar electrodynamics coupled to Einstein-Cartan gravity can be formulated as a constrained 3BF theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3BF action for the choice of a Lie 3-group corresponding to scalar electrodynamics is performed. This analysis is the first step towards a canonical quantization of a 3BF theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein-Cartan gravity formulated as a 3BF action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3BF theory for this choice of a 3-group is a topological field theory, as expected.

gr-qc↗

arXiv2019

Higher Gauge Theories Based on 3-groups

We study the categorical generalizations of a $BF$ theory to $2BF$ and $3BF$ theories, corresponding to $2$-groups and $3$-groups, in the framework of higher gauge theory. In particular, we construct the constrained $3BF$ actions describing the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl and Majorana fields coupled to Einstein-Cartan gravity. The action is naturally split into a topological sector and a sector with simplicity constraints, adapted to the spinfoam quantization programme. In addition, the structure of the $3$-group gives rise to a novel gauge group which specifies the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained $3BF$ action, facilitating the nonperturbative quantization of both gravity and matter fields. Moreover, the presence and the properties of this new gauge group open up a possibility of a nontrivial unification of all fields and a possible explanation of fermion families and all other structure in the matter spectrum of the theory.

hep-th↗