Defining determinism

The article puts forward a branching - style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of (differential) equations, one based on mappings between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping- and the equations - based approaches. After giving a detailed formal explication of a branching - based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching- and the mapping-based approach. We conclude that the branching - based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories

Noncommutative geometry and physics: a review of selected recent results

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.Comment: Based on lectures given at the TMR School on contemporary string theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on exterior product of n left-invariant one-forms corrected, small changes in the Sect. on integratio

A Simple Method for Computing Soliton Statistics

I provide an extremely simple argument that the kink-type solitons in certain theories are fermionic. The argument is based on the Witten index, but can in fact be used to determine soliton statistics in non-supersymmetric theories as well.Comment: 9 pages, harvmac, HWS-92/09. (Added substantial details in one section.

On the Deformation Quantization Description of Matrix Compactifications

Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A noncommutative description of these Yang-Mills theories based in deformation quantization theory is provided. We show that this framework allows a natural generalization of the `Moyal B-deformation' of the Yang-Mills theories to non-constant background B-fields on curved spaces. This generalization is described through Fedosov's geometry of deformation quantization.Comment: 25 pages, harvmac file, no figures, corrected typos, added references, one comment added in sec.

Bounded Arithmetic in Free Logic

One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not. In this paper, we reformulate Buss' theories using free logic and conjecture that such theories are easier to handle. To show this, we first prove that Buss' theories prove consistencies of induction-free fragments of our theories whose formulae have bounded complexity. Next, we prove that although our theories are based on an apparently weaker logic, we can interpret theories in Buss' hierarchy by our theories using a simple translation. Finally, we investigate finitistic G\"odel sentences in our systems in the hope of proving that a theory in a lower level of Buss' hierarchy cannot prove consistency of induction-free fragments of our theories whose formulae have higher complexity

The Place of the Trace: Negligence and Responsibility

One popular theory of moral responsibility locates responsible agency in exercises of control. These control-based theories often appeal to tracing to explain responsibility in cases where some agent is intuitively responsible for bringing about some outcome despite lacking direct control over that outcome’s obtaining. Some question whether control-based theories are committed to utilizing tracing to explain responsibility in certain cases. I argue that reflecting on certain kinds of negligence shows that tracing plays an ineliminable role in any adequate control-based theory of responsibility

Supersymmetric Gauge Theories with an Affine Quantum Moduli Space

All supersymmetric gauge theories based on simple groups which have an affine quantum moduli space, i.e. one generated by gauge invariants with no relations, W=0, and anomaly matching at the origin, are classified. It is shown that the only theories with no gauge invariants (and moduli space equal to a single point) are the two known examples, SU(5) with 5-bar + 10 and SO(10) with a spinor. The index of the matter representation must be at least as big as the index of the adjoint in theories which have a non-trivial relation among the gauge invariants.Comment: Incorrect proof that theories with constraints must have mu >= mu(adj) replaced by a correct one (6 pages, uses revtex, amssymb, array

Recola2: a one-loop matrix-element generator for BSM theories and SM effective field theory

We present the Recola2 library for the efficient generation and computation of one-loop amplitudes in Beyond-Standard-Model theories. Recola2 is based on Recola, an efficient one-loop amplitude generator for the Standard Model, and Rept1l, a newly developed tool to generate one-loop model files for Recola2 in a fully automated way. Recola2 is able to operate with non-trivial extensions of the SM, e.g. extended Higgs sectors and effective field theories. We discuss first applications to extended Higgs sectors and their renormalization.Comment: 6 pages, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017