A positive-definite scalar product for free Proca particle
نویسندگان
چکیده
منابع مشابه
Product of three positive semi-definite matrices
In [2], the author showed that a square matrix with nonnegative determinant can always be written as the product of five or fewer positive semi-definite matrices. This is an extension to the result in [1] asserting that every matrix with positive determinant is the product of five or fewer positive definite matrices. Analogous to the analysis in [1], the author of [2] studied those matrices whi...
متن کاملStrictly Positive Definite Functions on a Real Inner Product Space
Abstract. If f(t) = ∑∞ k=0 akt k converges for all t ∈ IR with all coefficients ak ≥ 0, then the function f(< x,y >) is positive definite on H ×H for any inner product space H. Set K = {k : ak > 0}. We show that f(< x,y >) is strictly positive definite if and only if K contains the index 0 plus an infinite number of even integers and an infinite number of odd integers.
متن کاملParticle Interpretations and Green Functions for a Free Scalar Field∗
The formalism of Ashtekar and Magnon [2] for the definition of particles in quantum field theory in curved spacetime is further developed. The relation between basic objects of this formalism (e.g., the complex structure) and different Green functions is found. It allows one to derive composition laws for Green functions. The relation of two definitions of particles is reformulated in the forma...
متن کاملScalar Product Graphs of Modules
Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...
متن کاملSpectrum of Positive Definite Functions on Product Hypergroups
This paper aims to show that the amenability of K1 ×K2 is equivalent to the following condition: “If φ is a continuous positive definite function defined on K1 ×K2 and φ ≥ 0 then the constant function 1K1×K2 belongs to the spectrum of φ”, which K1 and K2 are locally compact hypergroups as defined by R. Jewett [1], with convolutions ∗1, ∗2 respectively.Our study deals with the cases of exponenti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Journal of Physics
سال: 2006
ISSN: 0011-4626,1572-9486
DOI: 10.1007/s10582-006-0394-x