I have 2 elementary questions about your article “The Physics of Virtual

Particles”.

1. In the paragraph headed “

**States.**” on p. 4, of 13, you talk about states of a

physical system, with a mixed state specified by a Hermitian operator ρ of trace

1 acting on the Hilbert space of the system which contains the system’s pure

state vectors. You say that this also covers the pure case with ρ = ψψ*. Do the

symbols on the right-hand side of this equation indicate the product, in the

standard product of functions sense, of ψ with its complex conjugate? If so, for a

system consisting of just one particle, ρ is a function of the arguments

**r**and t of

ψ whose value at each (

**r**,t) is the probability density of finding the particle at the

point

**r**at time t in whatever space the argument

**r**of ψ is, e.g., position space or

momentum space. This ρ doesn’t sound like a Hermitian operator of trace 1, and

doesn’t even specify a state completely; for example, if the value of ρ is the

position probability density, ρ doesn’t determine the momentum probability

density, and vice-versa. Was this just a case of your using “ρ” for two different

things, that is, with two different meanings?

2. In the paragraph headed “

**Stable and unstable particles.**” on p. 5, you say

that stable particles, according to the QFT formalism, must be on-shell, meaning

that their momentum

*p*is related to the real rest mass mm (sic) (doubling due to

typo?) by the relation

*p*=

^{2}*m*(in units where

^{2}*c*= 1). You clearly were not talking

just about particles that move (in vacuum) only at speed

*c*(= 1 in your units). In

relativistic mechanics,

*p*=

^{2}*m*, where

^{2}v^{2}*m*is the relativistic (moving) mass, not

the rest mass, and

*v*= 1 (in your units) only for particles moving at speed

^{2}*c*. The

“

*v*" was omitted in that equation in 3 later paragraphs, in the first of which, for

^{2}complex

*p*and

*m*, after the equation “

*p*=

^{2}*m*", you have “and

^{2}*v*=

*p/m*real",

implying

*p*=

^{2}*m*. Is the omission of all those “

^{2}v^{2}*v*" ‘s due to a peculiarity of QFT,

^{2}to the fact that you were thinking just of particles moving with speed

*c*(= 1) when

you were writing this but neglected to specify that limitation, or is it just a strange

repeated typo or other similar error--or something else?

--fox26