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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.
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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.
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Published in 2021 at "Letters in Mathematical Physics"
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.
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Published in 2018 at "IMA Journal of Numerical Analysis"
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.
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Published in 2021 at "Quarterly Journal of Mathematics"
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degree theory, especially for Fredholm maps with positive index as developed with Tromba, is combined with Ramer’s unpublished thesis work on finite co-dimensional differential forms.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.
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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.
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Published in 2020 at "International Journal of Modern Physics A"
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.
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Published in 2021 at "Universe"
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.