Quasiconvexity and Relaxation in Optimal Transportation of Closed Differential Forms
Sign Up to like & getrecommendations! Published in 2019 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-019-01390-9
Abstract: This manuscript extends the relaxation theory from nonlinear elasticity to electromagnetism and to actions defined on paths of differential forms. The introduction of a gauge allows for a reformulation of the notion of quasiconvexity in… read more here.
Keywords: optimal transportation; differential forms; relaxation; quasiconvexity relaxation ... See more keywords
Conformally Covariant Bi-differential Operators for Differential Forms
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-019-03431-6
Abstract: The classical Rankin–Cohen brackets are bi-differential operators from $$C^\infty ({\mathbb {R}})\times C^\infty ({\mathbb {R}})$$ C ∞ ( R ) × C ∞ ( R ) into $$ C^\infty ({\mathbb {R}})$$ C ∞ ( R )… read more here.
Keywords: infty mathbb; covariant differential; conformally covariant; differential forms ... See more keywords
On a Batalin–Vilkovisky operator generating higher Koszul brackets on differential forms
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DOI: 10.1007/s11005-021-01383-4
Abstract: We introduce a formal $$\hbar $$ -differential operator $$\Delta $$ that generates higher Koszul brackets on the algebra of (pseudo)differential forms on a $$P_{\infty }$$ -manifold. Such an operator was first mentioned by Khudaverdian and… read more here.
Keywords: koszul brackets; operator; operator generating; differential forms ... See more keywords
Hierarchical B-spline complexes of discrete differential forms
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DOI: 10.1093/imanum/dry077
Abstract: In this paper we introduce the hierarchical B-spline complex of discrete differential forms for arbitrary spatial dimension. This complex may be applied to the adaptive isogeometric solution of problems arising in electromagnetics and fluid mechanics.… read more here.
Keywords: differential forms; spline complex; spline; spline complexes ... See more keywords
Infinite-Dimensional Degree Theory and Ramer’S Finite Co-Dimensional Differential Forms
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DOI: 10.1093/qmath/haab022
Abstract: Infinite-dimensional degree theory, especially for Fredholm maps with positive index as developed with Tromba, is combined with Ramer’s unpublished thesis work on finite co-dimensional differential forms. As an illustrative example, the approach of Nicolaescu and… read more here.
Keywords: differential forms; dimensional degree; finite dimensional; degree theory ... See more keywords
A Tale of two derivatives: Phase space symmetries and Noether charges in diffeomorphism invariant theories
Sign Up to like & getrecommendations! Published in 2018 at "Physical Review D"
DOI: 10.1103/physrevd.98.044009
Abstract: For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of… read more here.
Keywords: space; theory; tale two; phase space ... See more keywords
Hamiltonian of new general relativity using differential forms
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DOI: 10.1142/s0217751x2040014x
Abstract: In a recent work we derived the kinematic Hamiltonian and primary constraints of the new general relativity class of teleparallel gravity theories and showed that these theories can be grouped in 9 classes, based on… read more here.
Keywords: new general; differential forms; hamiltonian new; general relativity ... See more keywords
Co-Homology of Differential Forms and Feynman Diagrams
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DOI: 10.3390/universe7090328
Abstract: In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in light of recent developments. Feynman integrals enter in several perturbative methods for solving non-linear PDE, starting… read more here.
Keywords: differential forms; homology differential; forms feynman; feynman integrals ... See more keywords