Recent content by pavsic

Yes, it has never been ruled in, if by this you mean a generally accepted theory. Indeed, string theory has never reached the status of a universally accepted theory of quantum gravity and the unification of fundamental forces and particles. Initially hailed as a highly promising avenue of...

Thank you for sharing. This video is now few years old. Today the prevailing opinion seems to be that string theory is ruled out. I do not agree that string theory is dead and useless. It is an important pillar supporting the next stage in building a unified theory of forces and particles...

There is a significant challenge in higher-dimensional theories, including string theory, regarding how to render the extra dimensions unobservable. A commonly employed approach involves assuming that the extra dimensions are compact and small. However, we can sidestep the necessity...

In post 56 I wrote a single particle state $$|\Psi \rangle = \int d^3 {\bf x}\, \psi (t,{\bf x}) a^\dagger ({\bf x})|0 \rangle, $$ where ##\psi (t,{\bf x}) = \langle {\bf x}|\Psi (t,{\bf x}) \rangle ## is a complex valued wave packet profile, that is a wave function in the x-representation...

I am adopting that interpretation. Namely, ##\Sigma## is defined by the frame in which the observer is at rest. But because there exist the observers who are in relative motion, this means that each of them is associated with a different ##\Sigma##, the hypersurface on which the events observed...

The Foldy equation of my post 56 $$i \frac{\partial \psi}{\partial t}= \sqrt{m^2 -\nabla^2} \psi$$, in non relativistic approximation becomes the Schroedinger equation.

In my post 56, ##a({\bf x})## and ##a^\dagger ({\bf x})## are field operators, whilst ##\psi (t,{\bf x})## are complex valued wave functions ("wave packet profiles"), not operators.

Wave function makes sense in relativistic quantum field theory. Starting from the scalar quantum field ##\varphi(x)##, where ##x\equiv x^\mu = (t,{\bf x})##, we can construct the operators (see Jackiw: Diverse topics in theoretical and mathematical physics) $$a(t, {\bf x}) = \frac{1}{\sqrt{2}}...

I am using ##\delta^4 ({\bar x}' - {\bar x})##, where ##{\bar x} \equiv {\bar x}^\mu##, and, as I explained in the previous reply, ##\bar x^\mu= {P^\mu}_\nu x^\mu## is the projection of the spacetime point onto the hypersurface ##\Sigma##. This projection is also a spacetime...

I wrote: "Recall what is "space". It is just a time slice, i.e., a hypersurface oriented so the that , . But it can be oriented differently (or observed from another reference frame)." Here I meant the active (passive) Lorentz transformation. Active LT: In a given reference frame one can...

They pick out the position of a particle in space. Recall what is "space". It is just a time slice, i.e., a hypersurface ##\Sigma_\mu## oriented so the that ##\Sigma_\mu = (0,\Sigma_i)##, ##i=1,2,3##. But it can be oriented differently (or observed from another reference frame), so that also the...

Of course it works. As stated by Demystifier, one can write a two particle state as $$|{\bar x}_1,{\bar x}_2 \rangle ,$$ where ##{\bar x}_1## and ##{\bar x}_2## are the positions on a given simultaneity hypersurface ##\Sigma_\mu .## A generic state of ##N## particles is a superposition of...

Position can be defined with respect to a reference frame, i.e., on a "simultaneity hypersurface" ##\Sigma_\mu##. When passing from one reference frame to another, the hypersurface ##\Sigma_\mu## transforms as a Lorentz 4-vector. Position on the hypersurface can be denoted by a 4-vector ##{\bar...

In my paper "A Theory of Quantized Fields Based on Orthogonal and Symplectic Clifford Algebras", Advances in Applied Clifford Algebras, 22 (2012) 449-481, http://dx.doi.org/10.1007/s00006-011-0314-4, [http://arxiv.org/abs/arXiv:1104.2266] , it is shown that those two routes are conceptually not...

Last week I was skiing with my wife and two daughters in Slovenian mountains. Weather was fantastic all the time, with majestic view on the LANDSCAPE and the Adriatic coast. A unique experience, in spite of the fact that there are so many different landscapes possible in principle, and yet I was...