相关论文: How Clifford algebra can help understand second qu…
In a long series of works the author has demonstrated that the model named the {\it spin-charge-family} theory offers the explanation for all in the {\it standard model} assumed properties of the fermion and boson fields, as well as for…
In a long series of works, it has been demonstrated, that the {\it spin-charge-family} theory offers the explanation for all in the {\it standard model} assumed properties of the second quantized fermion and boson fields, offering several…
Fifty years ago the standard model offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation. There are…
This contribution presents properties of the second quantized not only fermion fields but also boson fields, if the second quantization of both kinds of fields origins in the description of the internal space of fields with the ''basis…
This article presents the description of the internal spaces of fermion and boson fields in $d$-dimensional spaces, with the odd and even "basis vectors" which are the superposition of odd and even products of operators $\gamma^a$. While…
Fermions with the internal degrees of freedom described in Clifford space carry in any dimension a half integer spin. There are two kinds of spins in Clifford space. The spin-charge-family theory,assuming even d=13+1, uses one kind of spins…
This talk discusses the achievements of the {\it spin-charge-family} theory. The project started in the year 1993 when trying to understand the internal spaces of fermions and bosons with the Grassmann algebra. Recognizing that the…
The article proposes the description of internal spaces of fermion (quarks and leptons and antiquarks and antileptons) and boson (photons, weak bosons, gluons, gravitons and scalars) second quantized fields in a unique way if they all are…
The Clifford odd and even "basis vectors", describing the internal spaces of fermion and boson fields, respectively, offer in even-dimensional spaces, like in $d=(13+1)$, the description of quarks and leptons and antiquarks and antileptons…
Fifty years ago the {\it standard model} offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation.…
Both algebras, Clifford and Grassmann, offer "basis vectors" for describing the internal degrees of freedom of fermions. The oddness of the "basis vectors", transferred to the creation operators, which are tensor products of the finite…
In Ref. [arXiv:1802.05554v3] one of the authors (N.S.M.B.) studies the second quantization of fermions with integer spin while describing the internal degrees of freedom of fermions in Grassmann space. In this contribution we study the…
We present in Part II the description of the internal degrees of freedom of fermions by the superposition of odd products of the Clifford algebra elements, either $\gamma^a$'s or $\tilde{\gamma}^a$'s, which determine with their oddness the…
The spin-charge-family theory, which is a kind of the Kaluza-Klein theories in $d=(13+1)$ --- but with the two kinds of the spin connection fields, the gauge fields of the two Clifford algebra objects, $S^{ab}$ and $\tilde{S}^{ab}$ ---…
The internal degrees of freedom of fermions are in the spin-charge-family theory described by the Clifford algebra objects, which are superposition of an odd number of $\gamma^a$'s. Arranged into irreducible representations of…
We further explore the idea that physics takes place in Clifford space which should be considered as a generalization of spacetime. Following the old observation that spinors can be represented as members of left ideals of Clifford algebra,…
The article studies the extension of the internal spaces of fermion and boson second quantized fields, described by the superposition of odd (for fermions) and even (for bosons) products of the operators $\gamma^ {a}$, to strings and odd…
More than 40 years ago the standard model made a successful new step in understanding properties of fermion and boson fields. Now the next step is needed, which would explain what the standard model and the cosmological models just assume:…
Although the internal spaces describing spins and charges of fermions' and bosons' second-quantised fields have such different properties, yet we can all describe them equivalently with the ``basis vectors'' which are a superposition of odd…
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of…