Related papers: Lagrangian Relations and Quantum $L_\infty$ Algebr…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
We link the recent theory of $L$-algebras to previous notions of Universal Algebra and Categorical Algebra concerning subtractive varieties, commutators, multiplicative lattices, and their spectra. We show that the category of $L$-algebras…
We study a special type of $E_\infty$-operads that govern strictly unital $E_\infty$-coalgebras (and algebras) over the ring of integers. Morphisms of coalgebras over such an operad are defined by using universal $E_\infty$-bimodules. Thus…
Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpanding. Mardare, Panangaden and Plotkin introduced 1-basic varieties as categories of quantitative algebras presented by quantitative equations.…
There exists a natural $L_\infty$-algebra or $Q$-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the $L_\infty$-algebra behind the jet space BV-BRST formulation to its minimal…
Adapting a recent work of Brannan et al., on extending graph $C^*$-algebras to Quantum graphs, we introduce "Quantum Quivers" as an analogue of quivers where the edge and vertex set has been replaced by a $C^*$-algebra and the maps between…
Constructivist lagrangian propiates a diverse approach to field theory. Introduce the set action. Consider fields families under a same symmetry group. The resulting fields set extends the standard atomist field theory to a whole field…
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples,…
We deduce, in a general background gauge, the counter-term Lagrangian for pure quantum gravity to one-loop order. As an application, we evaluate the leading quantum correction to the classical gravitational potential, generated by the…
The physical variables of classical thermodynamics occur in conjugate pairs such as pressure/volume, entropy/temperature, chemical potential/particle number. Nevertheless, and unlike in classical mechanics, there are an odd number of such…
Recently B. Hartwig and the second author found a presentation for the three-point $sl_2$ loop algebra via generators and relations. To obtain this presentation they defined an algebra $\boxtimes$ by generators and relations, and displayed…
While $L_\infty$ algebras are fundamental structures in differential geometry and mathematical physics, the geometric information encoded in such structures is often implicit. We address the following question: What constitutes a…
The scalar-tensor theories of gravity in spacetime dimensions $D+1>2$ are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the…
A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a…
We highlight the structure and properties of an abstract approach to quantum cosmology and gravity, dubbed $SU(\infty)$-QGR. Beginning from the concept of the Universe as an isolated quantum system, the main axiom of is the existence of an…
Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH^*(LG) and show that its multiplicative structure…
Algebraic theories, sometimes called equational theories, are syntactic notions given by finitary operations and equations, such as monoids, groups, and rings. There is a well-known category-theoretic treatment of them that algebraic…
We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding…
Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…