The method which unifies physics

The simultaneous consideration of these two things is very important since, for example, the Maxwell equations alone are generally covariant but they are not invariant with respect to the reparametrization and this is not the case if we consider the genuine Riemann metric alone. By this the central role of the gravitational field in a unified physics is defined.

Where D t is the Lie derivative along a stream of time. The stress tensor of the gravitational field can be written in the following form:. Where and for a density of kinetic and potential energy of the gravitational field we have the following expressions:. We pay attention to that the heat equation of Hamilton tightly connected with the solution of the Poincare conjecture can be written in our notation as follows:. Thus, we have there very interesting physical and mathematical problem to consider connection between gravity and topology in the new framework.

Since the scalar temporal field enters into the Lagrangians of the physical fields in the form of the gradient of the scalar field. Where a is a constant, this is internal symmetry that defines the law of energy conservation as a fundamental physical law of the universe which is true in all cases. Here we establish dynamical equations of the generalized electromagnetic field shortly gef which are defined by gef symmetry and describe a new form of matter which interacts only gravitationally dark matter [ 12 - 14 ].

The problem of invisible mass is acknowledged to be among the greatest puzzles of modern cosmology and field theory. The most direct evidence for the existence of large quantities of dark matter in the Universe comes from the astronomical observation of the motion of visible matter in galaxies. One neither knows the identity of dark matter nor whether there are one or more types of its structure elements.

Theory of everything

The most commonly discussed theoretical elementary particle candidates are a massive neutrino, a syper symmetric neutralino, and the axion. So, at the present time there is a good probability that the set of known fields is by no means limited to those fields. Moreover, we are free to look for deeper reasons for the existence of a new form of energy unusual in many respects. The parallel displacement of vector fields and V with bilateral symmetry can be produced only by a pair of connections and P jk i with bilateral symmetry. From the law of parallel displacement we have.

Being generalized the bilateral symmetry takes status of gef symmetry GL n, R with the law of transformation. Where V i j is the component of the operator U-1 inverse to the operatorU, For brevity, we use the matrix notation. We give general solution of this equation. Setting where get general solution of the equation in question. Let us introduce a tensor field but in what follows we shall consider the irreducible deviation tensor. Let us introduce electric and magnetic strength of the generalized electromagnetic field by the direct and inverse mapping.

The system of equations in question is simultaneous. This system of equations describes a new form of matter which is the structure element of the unified physics and has the characteristics of an entity known from the observations as Dark Matter. Spin is already a great unifying principle in the theoretical physics, but its potential is far from being exhausted.

In a Unified Physics the Spin dynamics includes the region of physical phenomena which are now investigated in the Standard Model. Thus, spin symmetry is geometrical internal symmetry which provides new and complete understanding of spin and, hence, theory of elementary particles as well. Here we derive equations of Spin dynamics and with this process introduce operators of electrical charge and neutrino charge and discuss some questions connected with this innovation [ 16 ].

The spin symmetry group is a general linear group GL 16, R that acts in the space of the spinning fields. We constructed a natural general covariant basis in the Lie algebra gl 2 n , R of GL 2 n , R and uncover spin as the bipolar structure on the group of spin symmetry GL 2 n , R [ 11 ]. The bipolar structure having two dual sets of commuting operators exists which define the Lie algebra of two dual groups S and. This result expresses in the mathematical form that the spinning field has internal angular momentum and magnetic momentum and spinning field is the space of the two-valued representation of the dual groups S and.

Let us define the positive definite scalar product and the auxiliary scalar product in the linear space in question as follows:. We can also define that a system of two spinning fields A and possesses the bilateral symmetry if. It is clear that the introduction of this causal structure is adjoined with the consideration of two independent real spinning fields. To understand this new situation it is important to recognize the following results.

Symplectic scalar products are invariant with respect to the transformations of the group SL 2, R called in what follows the group of pseudo charge symmetry.

[physics/] A Unified Approach to the Classical Statistical Analysis of Small Signals

The generators of this group h1, h2, h3 are represented by the real matrices which satisfy the following relations:. In what follows we should like to deal with eigenvectors of this operator and, hence, with a complex spinning field and its conjugated. It is very important to recognize that this provides the existence of the probability measure in the space of solutions of the spin dynamics equations for the complex spinning field [11].

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The Lagrangian of Spin dynamics associated with the customary representation of bilateral symmetry and invariant with respect to the time reversal takes the form. This shows that there is a natural probability measure in the space of solution of equation This fundamental result was originally recognized in [17] and now it gives us an opportunity to identify the operator with an operator of the electrical charge. Let Ai be components of the potential of the electromagnetic field a. The Lagrangian of interaction of the real spinning field with the electromagnetic field is.

Describes electromagnetic interactions and can be considered as a basis for chemistry because the real spinning field carries only electrical charge. For comparison, the Lagrangian 7 is a basis for the strong interaction [ 11 ]. The operator La is define as follows: The operator of the neutrino charge Q should be connected with the parity non-conservation and, hence, it is defined by the orientation of the physical manifold. We define the operator in the component form.

The Lagrangian of Spin. But it is remarkable that the Lagrangian 10 is invariant only with respect to the transformation generated by the operator of the electric charge.

We see that in one case the spinning field carries only the electrical charge but in the second case it carries the electrical charge, the neutrino charge and pseudo charge. In both the cases the spinning field carries the internal spin which is generated by the geometrical internal symmetry defined by the anti -symmetrical tensor field Sij obeying the equation We have no possibility to discuss here this important symmetry [ 11 ] to be anywhere in detail.

Foundations of a Unified Physics

Let us mention some results of the Unification. Of course, the principal result is the dynamical equations of the gravitational field, spinning field and generalized electro-magnetic fields which form the nucleus of the unified physics as a system and this system will reveal its internal content in the process of its exploitation. In addition, we should like to formulate the following theses as the evidence that New Physics is the Unified Physics.

It is discovered that in the Universe there are two causal structures the two natural clocks. One of them is defined by general solution of the equation of temporal field 1. Another solution and a new causal structure emerge as special solution of this equation. The new causal structure gives natural explanation of the confinement and the baryon number conservation.

Indeed, we cannot invoke the artificial concept of force to explain the confinement because for any force there is a more powerful one. But causality is something else again. The baryon number conservation simply expresses in the symbolic form the existence of the second causal structure and nothing else. The quark - lepton symmetry means that leptons live in the area of the usual causal structure and quarks live in the area of the new causal structure. Mutual transitions are possible.

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The role of the gravitational field in the physics of elementary particles is recognized since the polarization of spin symmetry spin cannot be discovered without the gravitational field. Spin dynamics can be considered as a new purely rational realization of the Standard Model derived from the only first principle.

The observed generations of quarks and leptons are different states of the complex spinning field and the number of these generations equals four. The spinning field describes the physical entity retaining the elementarity and is considered to be characterized solely by equation 12 , electrical charge and the internal spin in one case and equation 9 , pseudo charge, electric charge, neutrino charge and the internal spin in the other case.

The problem of Dark Energy is solved. Dark Energy is simply the energy of the gravitational field. The problem of Dark Matter is solved. Department of Energy Office of Science, where he led the design and first stages of implementation of the Facility for Advanced Accelerator Experimental Tests project and the beam delivery efforts for the linear collider. Unifying Physics of Accelerators, Lasers and Plasma is a must-have for every student and practitioner of accelerator science.

It is a quick reference guide and provides solid, intuitive discussions of what are often quite erudite concepts. I enthusiastically applaud this outstanding book. It fills a gap in the market and helps in developing a better understanding of the concepts used in the quest to build compact accelerators. It is an inspiring read that is suitable for both undergraduate and graduate students, as well as researchers in the field of plasma accelerators.

This field has become truly multidisciplinary where lasers and plasmas are featuring very prominently in new ideas for particle acceleration, focusing, and new light sources. Professor Seryi has covered the essential fundamentals of accelerators, lasers, and plasmas to prepare students for their research careers in modern science of particle accelerators. Beside many other exciting topics, in this concise and enjoyable work, Seryi reviews the key elements of classical accelerators, beam optics, radiofrequency acceleration and technology, synchrotron radiation, beam instabilities, x-ray free-electron lasers, plasma acceleration, cancer therapy, advanced beam manipulation methods, and concepts of high-energy colliders, while frequently taking glimpses into the future.

In this gem, Seryi, for the first time, discusses the three areas of accelerators, lasers, and plasmas from a unified perspective. It is a textbook for a cross-disciplinary course, but it is also perfectly suitable for self-study. Its contents are quite unique and of interest for students preparing for research in a very promising and growing direction.

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