# What is Relativistic qm: Definition and 15 Discussions

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to those comparable to the speed of light c, and can accommodate massless particles. The theory has application in high energy physics, particle physics and accelerator physics, as well as atomic physics, chemistry and condensed matter physics. Non-relativistic quantum mechanics refers to the mathematical formulation of quantum mechanics applied in the context of Galilean relativity, more specifically quantizing the equations of classical mechanics by replacing dynamical variables by operators. Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.
Key features common to all RQMs include: the prediction of antimatter, spin magnetic moments of elementary spin 1⁄2 fermions, fine structure, and quantum dynamics of charged particles in electromagnetic fields. The key result is the Dirac equation, from which these predictions emerge automatically. By contrast, in non-relativistic quantum mechanics, terms have to be introduced artificially into the Hamiltonian operator to achieve agreement with experimental observations.
The most successful (and most widely used) RQM is relativistic quantum field theory (QFT), in which elementary particles are interpreted as field quanta. A unique consequence of QFT that has been tested against other RQMs is the failure of conservation of particle number, for example in matter creation and annihilation.In this article, the equations are written in familiar 3D vector calculus notation and use hats for operators (not necessarily in the literature), and where space and time components can be collected, tensor index notation is shown also (frequently used in the literature), in addition the Einstein summation convention is used. SI units are used here; Gaussian units and natural units are common alternatives. All equations are in the position representation; for the momentum representation the equations have to be Fourier transformed – see position and momentum space.

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1. ### I What is the role of Relativistic QM?

In non-relativity then there is QM, but in relativistic regime then there is QFT. Then what is useful role of Relativistics QM nowaday, or it is only has a historical meaning?Does non-existance wave function in relativistic regime make RQM meaningless?
2. ### Best book on relativistic QM and QFT

I loved Modern Quantum Mechanics by Sakurai, where Quantum Mechanics is presented and worked out. Now I would like to proceed further, and learn about Relativistic Quantum Mechanics and Quantum Field Theory. I started by reading Sakurai's Advanced Quantum Mechanics, but later I found that the...
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### I What Happens When the Hamiltonian in Dirac's Equation Isn't Linear in Momentum?

When constructing a relativistic quantum mechanical equation, namely Dirac equation, what would happen if we choose the Hamiltonian so that it's not linear in the momentum operator and the rest energy? You could say, why don't try it yourself and see what happens? That's because my knowledge is...
4. ### B The Dirac equation and the spectrum of the hydrogen atom

I was reading that one of the successes of the Dirac equation was that it was able to account for the fine structure of some of the differences in the spectrum of the hydrogen atom. But the Dirac equation is about subatomic particles moving at relativistic velocities. But an electron around the...
5. ### I Particle number conservation and motivations for QFT

I've read that one of the primary motivations for the need for QFT is that quantum mechanics cannot account for particle creation/annihilation, however special relativity "predicts" that such phenomena are possible (clearly they have been observed experimentally, but I'm going for a heuristic...
6. ### What is frequency from a photon's perspective?

If a photon does not experience time, how can it change? Without change, how can it have frequency?
7. ### Does relativistic QM obey rotational symmetry?

SO(3) is subgroup of Poicare group.Does Relativistic Quantum Mechanics obey rotational symmetry.If it is,why we do not still keep the non-relativistic concept of angular momentum(orbit angular momentum plus spin) for relativistic concept of angular momentum,but we instead replace the concept by...
8. ### Conservation of relavistic energy

Problem statement, equations, and work done: A particle called a Kaon is moving at 0.8c through a detector when it decays into two pions. Kaon particle: mass = 493.7 MeV/c^2 Pion+: mass = 139.6 MeV/c^2 Pion0: mass = 135.0 MeV/c^2 1) Apply conservation of momentum/energy to determine the...
9. ### Probability Postulate in Relativistic QM?

In non-relativistic QM, the probability postulate works very well in position and momentum space. But, I have read that in relativistic QM (Dirac or QFT), the probability postulate in position space does not work because the corresponding probability density function is not Lorentz covariant...
10. ### Foundations of Relativistic QM

I'd liked to know whether the postulates of standard QM are still valid in Relativistic QM By postulates I mean what is ussually stated in texbooks as follows 1)Physical states are determined by a vector in sate space E 2)A measurable physical quantity A is described by an observable A acting...
11. ### 2d Wavepacket in relativistic QM

Dear users, I wonder if there is anybody who can give me a hint on how to handle the following situation: In the 2+1 dimensional Klein-Gordon equation with coordinates (t,x,y), I use as initial condition for \Psi(x,0) a spherically symmetric Gaussian. The relativistic dispersion relation...
12. ### How is the 4-momentum 4-vector defined in relativistic QM?

I've been wondering about relativistic quantum mechanics. Elsewhere I'm addressing some comments about this branch of physics but I have never studied it. Is the 4-momentum 4-vector defined in the same way in relativsitic QM or is there a difference? I'm wondering if the time component of...
13. ### Relativistic QM though maybe more of a math question

Hi, I'm a bit befuddled about something my lecturer wrote: S^{\dagger}\sigma_{\alpha}R_{{\alpha}\beta}B_{\beta}S=R_{{\alpha}\beta}B_{\beta}S^{\dagger}\sigma_{\alpha}S R is a 3x3 rotation matrix which transforms the magnetic field B between frames, sigma_alpha are the pauli...
14. ### Is Noldus's Approach a Radical Redefinition of Quantum Mechanics?

http://arxiv.org/abs/gr-qc/0508104 Towards a fully consistent relativistic quantum mechanics and a change of perspective on quantum gravity 17 pages, submitted to CQG "This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being...
15. ### Pseudo Scalar Relativistic QM problem

Hi there, I have a problem that I could really do with a little help on. I have a spin 1/2 particle in which the dirac eqtn reads: ( i {d} - \gamma V(x) - m ) \Phi = 0 (I am new to latex - the d is SLASHED and the gamma is GAMMA5 ) In a potential V(x,t) = 0 for...