Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of metric constant. This leads a more restricted class invariance coordinate transformation: The symmetry properties unimodular are governed transverse diffeomorphisms. Nevertheless, if conservation energy–momentum tensor imposed in gravity, relativity theory recovered additional ...

Optimization over l ×m× n integer 3-way tables with given line-sums is NP-hard already for fixed l = 3, but is polynomial time solvable with both l,m fixed. In the huge version of the problem, the variable dimension n is encoded in binary, with t layer types. It was recently shown that the huge problem can be solved in polynomial time for fixed t, and the complexity of the problem for variable ...

Infinite hyperplane arrangements whose vertices form a lattice are studied from the point of view of commutative algebra. The quotient of such an arrangement modulo the lattice action represents the minimal free resolution of the associated binomial ideal, which defines a toric subvariety in a product of projective lines. Connections to graphic arrangements and to Beilinson’s spectral sequence ...

Unimodular gravity is one of the oldest geometric theories and alternatives to general relativity. Essentially, it based on Einstein–Hilbert Lagrangian with an additional constraint determinant metric. It can be explicitly shown that unimodular recast as relativity in presence a cosmological constant. This fact has led many discussions equivalence both at classical quantum levels. Here, we pres...

A bstract We compare the path integral for transition functions in unimodular gravity and general relativity. In cosmological constant is a property of states that are specified at boundaries whereas relativity parameter action. Unimodular with nondynamical background spacetime volume element has time variable canonically conjugate to constant. Wave depend on satisfy Schrödinger equation. On co...

By computer search we show that the lattice Γ from [9] is the unique extremal even unimodular 72-dimensional lattices that can be constructed as proposed in [6].