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C. G. Bollini

Publications and source records attributed to C. G. Bollini.

16 recordsLinked to original sources
arXiv2017

The Tachyon Propagator

Following the canonical quantization procedure for a tachyon field, the usual Hamiltonian and the creation and annihilation operators are obtained. The observation that the mass hyperboloid $p^2-m^2=0$ is one-sheeted, as opposed to the case of bradyons where $p^2+m^2=0$ is two-sheeted, leads to the construction of a base which is unbounded for negative as well as for positive energies. There is a zero-energy eigenfunction from which all other states can be constructed by repeated application of decreasing or increasing operators, within this Fock space the vacuum expectation value of the chronological product of field operators is shown to coincide with Cauchy's principal-value Green's function.

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arXiv2017

The Tachyon Field below the mass barrier

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have them a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof [4] that the total propagator is the Wheeler Green function [4,7].

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arXiv2013

A Solution to Non-Linear Equations of Motion of Nambu-Goto String

In this paper we solve the non-linear Lagrange's equations for the Nambu-Goto closed bosonic string. We show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field theories. We also prove that the string field is a linear superposition of UET of compact support (CUET), and give the notion of anti-string. We evaluate the propagator for the string field, and calculate the convolution of two of them.

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arXiv2010

Study of the Wheeler Propagator

We study the half advanced and half retarded Wheeler Green function and its relation to Feynman propagators. First for massless equation. Then, for Klein-Gordon equations with arbitrary mass parameters; real, imaginary or complex. In all cases the Wheeler propagator lacks an on-shell free propagation. The Wheeler function has support inside the light-cone (whatever the mass). The associated vacuum is symmetric with respect to annihilation and creation operators.

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arXiv2010

World Sheet Superstring and Superstring Field Theory: a new solution using Ultradistributions of Exponential Type

In this paper we show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way world sheet superstring and superstring field theories. A new Lagrangian for the closed world sheet superstring is obtained. We also show that the superstring field is a linear superposition of UET of compact support (CUET), and give the notion of anti-superstring. We evaluate the propagator for the string field, and calculate the convolution of two of them.

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arXiv2009

Bosonic String and String Field Theory: a solution using the holomorphic representation

In this paper we show that the holomorphic representation is appropriate for description in a consistent way string and string field theories, when the considered number of component fields of the string field is finite. A new Lagrangian for the closed string is obtained and shown to be equivalent to Nambu-Goto's Lagrangian. We give the notion of anti-string, evaluate the propagator for the string field, and calculate the convolution of two of them.

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arXiv2008

Superstring and Superstring Field Theory: a new solution using Ultradistributions of Exponential Type

In this paper we show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way superstring and superstring field theories. A new Lagrangian for the closed superstring is given. We show that the superstring field is a linear superposition of UET of compact support, and give the notion of anti-superstring. We evaluate the propagator for the superstring field, and calculate the convolution of two of them.

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arXiv2007

Bosonic String and String Field Theory: a solution using Ultradistributions of Exponential Type

In this paper we show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field theories. A new Lagrangian for the closed string is obtained and shown to be equivalent to Nambu-Goto's Lagrangian. We also show that the string field is a linear superposition of UET of compact support CUET). We evaluate the propagator for the string field, and calculate the convolution of two of them.

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arXiv2007

Convolution of Ultradistributions, Field Theory, Lorentz Invariance and Resonances

In this work, a general definition of convolution between two arbitrary Ultradistributions of Exponential type (UET) is given. The product of two arbitrary UET is defined via the convolution of its corresponding Fourier Transforms. Some examples of convolution of two UET are given. Expressions for the Fourier Transform of spherically symmetric (in Euclidean space) and Lorentz invariant (in Minkowskian space) UET in term of modified Bessel distributions are obtained (Generalization of Bochner's theorem). The generalization to UET of dimensional regularization in configuration space is obtained in both, Euclidean and Minkowskian spaces As an application of our formalism, we give a solution to the question of normalization of resonances in Quantum Mechanics. General formulae for convolution of even, spherically symmetric and Lorentz invariant UET are obtained and several examples of application are given.

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arXiv2003

Convolution of Lorentz Invariant Ultradistributions and Field Theory

In this work, a general definition of convolution between two arbitrary four dimensional Lorentz invariant (fdLi) Tempered Ultradistributions is given, in both: Minkowskian and Euclidean Space (Spherically symmetric tempered ultradistributions). The product of two arbitrary fdLi distributions of exponential type is defined via the convolution of its corresponding Fourier Transforms. Several examples of convolution of two fdLi Tempered Ultradistributions are given. In particular we calculate exactly the convolution of two Feynman's massless propagators. An expression for the Fourier Transform of a Lorentz invariant Tempered Ultradistribution in terms of modified Bessel distributions is obtained in this work (Generalization of Bochner's formula to Minkowskian space). At the same time, and in a previous step used for the deduction of the convolution formula, we obtain the generalization to the Minkowskian space, of the dimensional regularization of the perturbation theory of Green Functions in the Euclidean configuration space given in ref.[12]. As an example we evaluate the convolution of two n-dimensional complex-mass Wheeler's propagators.

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arXiv2003

Convolution of n-dimensional Tempered Ultradistributions and Field Theory

In this work, a general definition of convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. In the four-dimensional case, when the Tempered Ultradistributions are even in the variables $k^0$ and $ρ$ (see Section 5) we obtain an expression for the convolution, which is more suitable for practical applications. The product of two arbitrary even (in the variables $x^0$ and $r$) four dimensional distributions of exponential type is defined via the convolution of its corresponding Fourier Transforms. With this definition of convolution, we treat the problem of singular products of Green Functions in Quantum Field Theory. (For Renormalizable as well as for Nonrenormalizable Theories). Several examples of convolution of two Tempered Ultradistributions are given. In particular we calculate the convolution of two massless Wheeeler's propagators and the convolution of two complex mass Wheeler's propagators.

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arXiv1998

The Wheeler Propagator

We study the half advanced and half retarded Wheeler Green function and its relation to Feynman propagators. First for massless equation. Then, for Klein-Gordon equations with arbitrary mass parameters; real, imaginary or complex. In all cases the Wheeler propagator lacks an on-shell free propagation. The Wheeler function has support inside the light-cone (whatever the mass). The associated vacuum is symmetric with respect to annihilation and creation operators. We show with some examples that perturbative unitarity holds, whatever the mass (real or complex). Some possible applications are discussed.

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arXiv1998

Convolution of Ultradistributions and Field Theory

In this work, a general definition of Convolution between two arbitrary Tempered Ultradistributions is given. When one of the Tempered Ultradistributions is rapidly decreasing this definition coincides with the definition of J. Sebastiao e Silva. The product of two arbitrary distributions of exponential type is defined via the Convolution of its corresponding Fourier Transforms. Several examples of Convolution of two Tempered Ultradistributions and singular products are given. In particular, we reproduce the results obtained by A. Gonzales Dominguez and A. Bredimas.

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arXiv1996

Is the Higgs a visible particle ?

We suggest that the Higgs might be unobservable as a free particle, due to its origin at a symmetry breaking mechanism. The standard model is kept intact, only the definition of the vacuum for the Higgs is changed. With the new (natural) definition, the Higgs propagator is half advanced and half retarded. This Green function is compatible with the absence of free particles.

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arXiv1996

Non-Local Pseudo-Differential Operators

We define, in a consistent way, non-local pseudo-differential operators acting on a space of analytic functionals. These operators include the fractional derivative case. In this context we show how to solve homogeneous and inhomogeneous equations associated with these operators. We also extend the formalism to d-dimensional space-time solving, in particular, the fractional Wave and Klein-Gordon equations.

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