Related papers: Quantifier Elimination For Tame Fields
We show that any positive characteristic tame Hahn field $\mathbb{F}((t^\Gamma))$ containing $t$ is decidable in $\mathcal{L}_t$, the language of valued fields with a constant symbol for $t$, if $\mathbb{F}$ and $\Gamma$ are decidable. In…
In this paper, we prove a semistable reduction type theorem for multi-filtered vector spaces (or known as multi-weighted vector spaces).
Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $M_n(K)$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is used…
We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified…
We generalize Killing equations to a test particle system which is subjected to external force. We relax the conservation condition by virtue of reparametrization invariance of a particle orbit. As a result, we obtain generalized Killing…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of…
A temporal constraint language is a set of relations that are first-order definable over (Q;<). We show that several temporal constraint languages whose constraint satisfaction problem is maximally tractable are also maximally tractable for…
The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand, to periodic systems on the other. Boundary conditions are…
The mathematical description of stable particle-like systems appearing in relativistic quantum field theory at large, respectively small scales or non-zero temperatures is discussed.
We show that all finite dimensional, tame hereditary $k$-algebras are of amenable representation type (in the sense of G. Elek) for all fields $k$. The proof is adapted from our previous result for tame path algebras. Further, it is proven…
There is a large class of classical null-fronted metrics in which a free scalar field has an infinite number of conservation laws. In particular, if the scalar field is quantized, the number of particles is conserved. However, with more…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
We study the quantization of certain classical field theories using reflection positivity. We give elementary conditions that ensure the resulting vacuum state is cyclic for products of quantum field operators, localized in a bounded…
We study the quantum Hamiltonian reduction for affine superalgebras in the twisted case. This leads to a general representation theory of all superconformal algebras, including the twisted ones (like the Ramond algebra). In particular, we…
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
Let K be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map.…
Today's quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for $\varphi^4_4$ leading only to a "free" result. Affine quantization (AQ), an alternative quantization procedure, leads to a "non-free" result…