After WW2 as I know Japan capitulated and was disarmed. And as I know Japan was not able to have its own army, and its boundary should be protected by the United States. So, does Japan have the right to have its own army or navy? I was not able to find any worthy information in Google or Bing.
There are basically two answers to your question. The first comes from the legal precedents in the Japanese constitution, peace treaties, etc. The second is the de facto version of what actually happened after the war, and up to now.
Legally speaking, Japan was forbidden from having any kind of standing army, though they were permitted to have forces for their own self defense. Japan has never relied on the United States or any other country or governing body for its own protection in a strictly legal sense. In other words, the United States or United Nations never signed anything saying they would protect Japan.
However, in reality Japan does have a standing army in the form of its Self Defense Forces. Their military expenditures are in the top 10, and it is one of the most advanced armies in the world technologically, but still very small in terms of the number of people. The main difference after WWII is that Japan pledged never to deploy their forces abroad for any reason, though in the past 10-15 years they have been involved in some overseas peacekeeping, and contributed a destroyer and a refueling ship as a support asset to the war in Afghanistan. At this point, if Japan decided to increase the size of its military it wouldn't really be forbidden from doing so, but Japan has kept its military small by choice because, frankly, it's much cheaper.
Finally, while the United States never formally agreed to protect Japan the number of US military bases in the country means that, in a practical sense, it does. This has also allowed Japan to get away with keeping its military small, since the US Navy and other assets are spread all around Japan and S Korea. As far as the future goes, it's harder to say because the US has been rolling back military expenditures. It wouldn't be surprising to see the US encouraging Japan to increase the size of its military in order to decrease reliance on the US for protection, but it could easily go either way.
Formally, Japan has no right: http://en.wikipedia.org/wiki/Article_9_of_the_Japanese_Constitution#Debate
Substantively, the Japanese state has taken such a right: http://en.wikipedia.org/wiki/Japan_Self-Defense_Forces#History
Politically, as the Chinese state has a great interest in Japan's capacity for aggressive war, Japan's interpretation of Article 9 both formally and substantively is closely watched by a large heavily armed state.
Security Challanges: Japan’s Defence Dilemma is an interesting document. It sheds some light on this history of balancing constitution (and anti-militaristic sentiment associated), Japan's strategic objectives and it's alliance with the United State. It takes the view that Japan have been subverting article 9 to "normalise" the state. It also points out that major problem with extending the role of the JSDF (or "Normalising" its role) would be to "normalise" the relationship with the US and perhaps risk losing the US's large protective presence. However it also questions how much Japans refusal to take a normal military role may already be jeopardizing it's relation with the US. It's an interesting view and seems to echo what the other answerers are saying.
Here's an extract:
Normalisation by Stealth
The entire course of Japan’s post-war defence policy has been a slow march towards normalcy. In practice, Japan’s so-called ‘peace constitution’ has only delayed but not prevented progress towards normal statehood. Initially, successive Japanese governments engaged in a process of ‘revision by reinterpretation’ as a way of circumventing constitutional prohibitions. More recently ‘revision by legislation’ has been the preferred method of change. Both the Iraq deployment and the dispatch of naval forces to the Indian Ocean in support of the coalition in Afghanistan have been authorised by specific items of legislation in 2001 and 2003. These capped a series of laws enacted over the past decade, which have expanded and diversified the roles and capabilities of Japan’s Self-Defence Forces (SDF). Successive Japanese governments have accumulated a series of faits accomplis, creating the necessary precedents for the acquisition of new functions by the SDF.
2 Article 9 of the Japanese Constitution – the so-called ‘Peace Clause’ – has been consistently interpreted by the Japanese government as prohibiting Japan’s exercise of its right to collective self-defence (meaning military action to defend the United States or its forces) as well as Japanese participation in collective security operations under UN auspices. However, Japan’s inherent right to collective self-defence as a sovereign state has never been abrogated, and indeed is recognised under the UN charter. The prevailing interpretation of Article 9 on collective self-defence was made in 1981 by the Cabinet Legislation Bureau. It stated: ‘It is recognized under international law that a state has the right of collective self-defense, which is the right to use actual force to stop an armed attack on a foreign country with which it has close relations, even when the state itself is not under direct attack. It is therefore self-evident that since it is a sovereign state, Japan has the right of collective self-defense under international law. The Japanese government nevertheless takes the view that the exercise of the right of self-defense as authorized under Article NINE of the Constitution is confined to the minimum necessary level for the defense of the country. The government believes that the exercise of the right of collective self-defense exceeds that limit and is not, therefore, permissible under the Constitution’. Quoted in R J Samuels, ‘Constitution al Revision in Japan: The Future of Article 9’, The Brookings Institution, Center for Northeast Asian Policy, 15 December 2004, www.brookings.edu/fp/cnaps/events/20041215.pdf.