Zsolt68 írta:liederivative írta:Cím: Relativisztikus dinamika és a nyugalmi tömeg változása
Megismétlem a kérdést:
Ha az energia görbíti a téridőt, mi köze van ehhez a Higgs-mechanizmusnak?
Azt értem, hogy a skalárpotenciál tömegként jelenik meg a mozgásegyenletekben.
Na de hogyan lesz ebből a téridőt meggörbítő energia?
Erre nem teljesen egyértelmű a válasz szerintem, és a nem túl jól definiált gravitációs energiát is tekintetbe vehetjük (api ír a gravitációs energiáról az itteni jegyzetében, én nagyon bonyolult fogalomnak tartom).
1.
https://www.researchgate.net/post/What- ... -spacetime A válaszok különböző szerzőktől származnak, akiket a fenti linken megtalálhatsz.
"The space-time geometry is determined by the energy-momentum tensor of all the matter field, by virtue of Einstein's equation in general relativity. If the Higgs field is zero in a region, then all particles (fermions + bosons) would have zero rest mass as predicted by the Standard Model. Therefore, the space-time geometry in this region will be determined by the energy-momentum tensors of zero rest mass particles as well as that of the Higgs field potential. This geometry will be fundamentally different from the case when the Higgs field has acquired the vacuum expectation value due to the spontaneous symmetry breaking, because of which fermions and gauge bosons (except for photons and gluons) acquire masses. Thus, space-time geometry is indeed linked with the dynamics of the Higgs field."
"In Einstein's gravity, gravitational interaction is related with changes in the space-time geometry through Einstein's equation, Gμν + Λgμν= (8πG/c4)Tμν which contains Einstein's cosmological constant term Λ. This is a classical equation. However, there are many investigations on the subject of what could be the possible origin of Λ term in the context of a quantum field theory. In such discussions we find that Λ is related with the vacuum energy which has mainly three contributions
Zero point energy of quantum fields
Contribution from Higgs VEV
QCD contribution"
"These contributions cancel out to give a small value of Λ. Exact mechanism of such cancellation is not known. Some anthropic arguments are generally forwarded."
From General Relativity (GR) point of view Higgs field is matter field.
Actually form GR point of view everything is matter fields except of gravity. The gravity is space-time geometry.
Einstein equation relates geometry (Einstein tensor) with energy-momentum tensor of matter fields ("and the mass causes space-time distortion").
Contributions of Higgs field to e-m tensor are
1) Contribution of uniform Higgs background. It looks like exactly as contribution to vacuum energy or to cosmological term.
2) Contribution of Higgs field excitations (Higgs bosons) is similar to contribution from any other particles.
3) Energy of interaction of uniform Higgs background and massive particles contributes to particle masses. It contribute to e-m tensor through particle contributions."
"It is a scalar field or a scalar function of space-time points. That is each point in 4-D world has a number determined by the function φ(x,y,z,t). This field is not something arbitrary, rather it is characterized by it's coupling with fermions and gauge bosons. Also, the Higgs potential can only contain up to the fourth power of this field, on mass dimensional grounds, which will keep it's coupling strengths (Yukawa, quartic) dimensionless."
"A more complex answer to your question can be given in terms of the representations of Poincare group SO(1,3) x R4. We label one particle quantum states by representations of SO(1,3) having specific energy-momentum which generates translation in R4. Representations are scalar, vector, spinor (left and right handed), Dirac spinor, Spin-2 graviton and so on, each representation is further labeled by it's location in R4. For example, when I write φ(x,y,z,t), it carries two meanings simultaneously. It is a Lorentz scalar which is located at the space-time point (x,y,z,t).
Higgs boson is a "missing link" in the sense that we already had observed vector and spinor representations in high energy experiments in the form of gauge bosons and fermions. The scalar representation looks simple in terms of mathematics but very complex in terms of experimental search. At last it was discovered in 2012 at CERN-LHC."
"The space-time geometry is determined by the energy-momentum tensor of all the matter field, by virtue of Einstein's equation in general relativity. If the Higgs field is zero in a region, then all particles (fermions + bosons) would have zero rest mass as predicted by the Standard Model. Therefore, the space-time geometry in this region will be determined by the energy-momentum tensors of zero rest mass particles as well as that of the Higgs field potential. This geometry will be fundamentally different from the case when the Higgs field has acquired the vacuum expectation value due to the spontaneous symmetry breaking, because of which fermions and gauge bosons (except for photons and gluons) acquire masses. Thus, space-time geometry is indeed linked with the dynamics of the Higgs field."
Általánosan a szemiklasszikus és a QG-tárgyalásoknál precízebben kell szerintem eljárnunk, és nincs igazi válasz, amíg QG sincs.
Mondjuk,
https://en.wikipedia.org/wiki/Quantum_f ... _spacetime Itt a gravitációs mező adott lehet, és részecskék keletkeznek.
"In theoretical physics, quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory treats spacetime as a fixed, classical background, while giving a quantum-mechanical description of the matter and energy propagating through that spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. The most famous example of the latter is the phenomenon of Hawking radiation emitted by black holes.
Ordinary quantum field theories, which form the basis of standard model, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth. In order to describe situations in which gravity is strong enough to influence (quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime. These theories rely on general relativity to describe a curved background spacetime, and define a generalized quantum field theory to describe the behavior of quantum matter within that spacetime.
For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles.[1] Only in certain situations, such as in asymptotically flat spacetimes (zero cosmological curvature), can the notion of incoming and outgoing particle be recovered, thus enabling one to define an S-matrix. Even then, as in flat spacetime, the asymptotic particle interpretation depends on the observer (i.e., different observers may measure different numbers of asymptotic particles on a given spacetime).
Another observation is that unless the background metric tensor has a global timelike Killing vector, there is no way to define a vacuum or ground state canonically. The concept of a vacuum is not invariant under diffeomorphisms. This is because a mode decomposition of a field into positive and negative frequency modes is not invariant under diffeomorphisms. If t′(t) is a diffeomorphism, in general, the Fourier transform of exp[ikt′(t)] will contain negative frequencies even if k > 0. Creation operators correspond to positive frequencies, while annihilation operators correspond to negative frequencies. This is why a state which looks like a vacuum to one observer cannot look like a vacuum state to another observer; it could even appear as a heat bath under suitable hypotheses."
Szerző: Zsolt68 » 2022.07.14. 06:45 
RE: Zsolt offtopikja
RE: Zsolt offtopikja