Solutions to the Thirring model are constructed in the framework of algebraic quantum field theory. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is λ = 2(2n + 1)π, n ∈ N, otherwise solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces, so the whole Hilbert space becomes non-separable and in eac...

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no ultrafilter ...

In the Hyperbolic space Hn (n ≥ 3) there are uncountably many topological types of convex hypersurfaces. When is a locally convex hypersurface in Hn globally convex, that is, when does it bound a convex set? We prove that any locally convex proper embedding of an (n− 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n−1)-flats of the resulting hypersu...

Using combinatorial methods, we prove the following theorem on the group S of all permutations of a countably-infmite set: Whenever p 6 S has infinite support without being a fixed-point-free involution, then any s G S is a product of three conjugates of p. Furthermore, we present uncountably many new conjugacy classes C of S satisfying that any s G S is a product of two elements of C. Similar ...

These notes discuss sets, mappings between sets, and the notion of countably infinite. This material supplements the lecture on countably and uncountably infinite sets in the EE 503 probability class. The material is useful because probability theory is defined over abstract sets, probabilities are defined as measures on subsets, and random variables are defined by mappings from an abstract set...

In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with only finite extensions up to isomorphism. The verification consists in gathering known results about automorphism groups and Galois cohomology. This contrasts recent discovery by A. Bot an affine uncountably

There is one-to-one correspondence between quadratic operators (mapping $${\mathbb {R}}^m$$ to itself) and cubic matrices. It known that any operator corresponding a stochastic (in fixed sense) matrix preserves the standard simplex. In this paper we find conditions on (non-stochastic) ensuring Moreover, construct several non-stochastic which generate chaotic dynamical systems These behaviors ar...

In this paper, we revisit Arveson's characterisation of CCR flows in terms the decomposability product system multiparameter context. We show that a E0-semigroup is flow if and only it decomposable admits unit. contrast to one parameter situation, exhibit uncountably many examples E0-semigroups which do not admit any As applications, for pure isometric representation V, associated αV remembers ...

The phase retrieval problem arises when a signal must be reconstructed from only the magnitude of its Fourier transform; if the phase information were also available, the signal could simply be synthesized using the inverse Fourier transform. In continuous phase retrieval, most previous solutions rely on discretizing the problem and then employing an iterative algorithm. We avoid this approxima...