As Britain's cycling success has grown and grown, so Peters' work with track racing's two most high-profile athletes, Victoria Pendleton and Sir Chris Hoy, has become relatively well known. After all, when Pendleton calls Peters "the most important person in my career", or Hoy says that "without Steve I don't think I could have brought home triple gold from Beijing", people tend to take notice.
At the 2012 Games, it will be Peters' job as British Cycling's "head coach" – as he is known inside the team, pun fully intended – to make sure the riders who will spearhead Britain's medal hopes are as successful as possible.
At the London Olympic test event the weekend before last, just as at almost every major GB track engagement since before Athens 2004, Peters' slight, silver-haired figure could be seen, hovering on the wings of the British contingent. Given that he was one of the four-man core management team in Beijing for the all-conquering GB cycling squad, and given the success of his work in other sports – "around 10 right now," he says – one imagines his presence alone is reassuring to the riders.
This summer, Peters will be in the same velodrome in Stratford, east London, in the same role. But he recognises that the stakes will be way higher than usual for his charges, higher than any before. Hence the "ghosts".
"People look to the Olympics as a special event," Peters says, "and it's quite self-evident to say that London is going to create an enormous spotlight on our particular athletes. For most of the athletes in Olympic disciplines, they've got one shot every four years and that's quite critical compared to other sports, where there are tournaments going on every week."
So intense is the pressure that Peters has created special "coping strategies" that are designed to handle both failure and success in London.
"We have a policy in place for those who are possibly doing a swansong in London," he says, "and what options they have after the Olympics. But we also have safety nets in place for those who don't perform so well, or for those who perform really well and then you have this dive after the Olympics, which is what we saw after Beijing."
Peters' work has already helped to ensure that, despite the British team having done so well in Beijing, there has been no collective increase in their fear of failure.
"Not at all. What we've done as a team is say, 'Wipe out the past, it's a level playing field'," he explains. "Don't forget, in cycling they've changed some of the events and limited us to one athlete per event. We cannot achieve what we did in Beijing" – eight gold medals, four silver and two bronze – "it's not possible. So therefore we're coming to do our best and deliver what we can."
Cycling has its own psychological pressures, Peters says, "because [imagine] you're a cyclist and miss other sprinters making a breakaway move. There's a lot of tactical stuff. But a 100-metre sprinter just looks at his own start, his own lane. The rest don't bother him."
"And in snooker" – Peters works with the former world champion Ronnie O'Sullivan – "missing an easy ball means you may have to sit there listening to your opponent clinking away at the balls. The pressures in each sport are totally different and each cyclist has very different concepts of what pressure is. There is no single recipe book."
Talking of books takes us neatly round to the one that Peters has just published, The Chimp Paradox. Put in a nutshell, this is the mind-management programme that lies at the heart of much of Peters' work, in which the irrational, emotional side of a personality is depicted as a chimp. Peters' book teaches you how to "train" your chimp, despite it being stronger than the rational "you".
One fan is Sir Chris Hoy. However, Peters is at pains to point out that there is "nothing on sport in this book".
"What I normally do with athletes," he says, "as I do with anybody who comes to me, is [to say to them], 'Can we understand what's going on in your head, what sort of machine are we working with? So the book asks you to 'discover' your machine and then it's a question of where you want to apply it. That's the same for everybody.
"And clearly I do not want to give away anything before the Olympic Games, on how I deal with elite sport. That was never going to happen."
The Chimp Paradox is refreshingly free of psychobabble, making it very accessible. This is something Peters says is probably due to his background in education.
"I've been a lecturer at Sheffield University for 20 years now," he says, "and when you're teaching doctors it's very important to get your ideas across simply and effectively so they can use them in a practical way."
Peters says he has "cheated a bit by simply saying there's a chimp and a human", because in fact there are between six and 10 different bits of the brain that "think". But that would be too hard to explain. "The chimp, on the other hand, is a concept everybody can grasp and which is usable."
If Peters is giving away nothing about how he treats athletes prior to London 2012, he does reveal the areas in which he operates with them. It's what he calls the "15 per cent" that makes the difference between a good athlete and a brilliant one who might, say, win three gold medals at one Games, à la Hoy.
"If people are functioning at an 85 per cent level of their capacities," he says, "they tend to be happy and complacent and say, 'I'm doing really well, I'll skip the last 15 per cent.' But that's where the trivial details [that make the difference], such as being slightly overweight, tend to be.
"But I would say there are some very astute people around, and Chris Hoy is one of them, who recognises there are mental areas where he could improve. So he comes along and he says to me, 'Give me the extra 15 per cent. I want to be at 100'."
Hoy, Peters says, was far from falling apart at the seams when he first met him. "This was a man who was fully with it. But he recognised he could get an extra bit out of my training by using mental skills. He learnt those skills, he moved from 85 per cent to 100."
Peters also points out that this does not mean his athletes become obsessive through working with him. "It's perhaps the opposite. Normally at 100 per cent they're more relaxed."
You could say that the "chimp concept" sounds a shade childish. Peters agrees that it sounds amusing, not to mention unthreatening, but says that is intentional, if only to a degree.
"The model I've invented is fun, but... it has a very serious side. My intention [in the book] is to give some quality of life to a lot of people who are struggling to get that. But I don't want it to come across as if this is some amazing concept that I've produced and if you don't use it then there's something wrong with you."
The success of Peters' "Chimp Paradox" with Britain's cyclists, however, is a rather convincing argument in his favour. This summer, if London 2012 works out as planned, Peters may well find he has created another.
'The Chimp Paradox: The Mind Management Programme to Help You Achieve Success, Confidence and Happiness', by Dr Steve Peters, is published by Vermilion, priced £11.99