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The goal of this paper is to define the Grassmann integral in terms of a limit of a sum around a well-defined contour so that Grassmann numbers gain geometric meaning rather than symbols. The unusual rescaling properties of the integration of an exponential is due to the fact that the integral attains the known values only over a specific set of contours and not over their rescale
It is demonstrated how quantum mechanics is generated by stochastic momentum kicks from the force carriers, transmitting the fundamental interactions between the point particles. The picture is consistent with quantum field theory and points out that
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers which are oriented hypergraphs. We describe mutations of such objects and d
The definitions of para-Grassmann variables and q-oscillator algebras are recalled. Some new properties are given. We then introduce appropriate coherent states as well as their dual states. This allows us to obtain a formula for the trace of a opera
Earlier comparisons of galatic rotation curves with MOND have arrived at the conclusion that the parameter a_0 lies within ~20% of cH_0/2pi, where c is the velocity of light and H_0 is the Hubble constant. It is proposed here that, for this value of
In this paper we will utilize the non-trivial shapes of the strings in order to come up with realistic definition of probability amplitudes in a lot more natural way than could be done in point particle counterpart. We then go on to translate GRW mod